Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

Tutors Answer Your Questions about Sequences-and-series (FREE)

Question 195098: Find the missing term of each geometric sequence.
26. 16, [?] , 4
27. 25, [?] , 225

28. 2, [?] , 50
29. 1, [?] , 49
30. 3/4, [?] , 3
31. 36, [?] , 4
Click here to see answer by Edwin McCravy(8912)

Question 195095: 4. On October 1, a gardener plants 20 bulbs. On October 2, she plants 23
bulbs. On October 3, she plants 26 bulbs. She continues in this pattern
until October 15, on which she plants the last bulbs.
a. Write an explicit formula to model the number of bulbs she plants
each day.
b. Write a recursive formula to model the number of bulbs she plants
each day.
c. How many bulbs will the gardener plant on October 15?
d. What is the total number of bulbs she plants from October 1 to
October 15, inclusive?
Click here to see answer by RAY100(1637)

Question 195293: fill in the terms so that the following sequence is arithmetic.
4,-, -,-,166
please help me to solve please.... help
Click here to see answer by solver91311(16897)

Question 195291: write amn explicit formula for the following infinite sequence 14,17,20,23.....
Click here to see answer by jim_thompson5910(28598)

Question 195585: please i need help on these question can any one help me????
please help......
1)Find the 111th term of an arithmetic sequence that has a first term of an arithmetic sequence that has a first term of 4 and a common difference of -0.8
2)Write the following series in summation notation. Use i as index variable and start I at 1 2+4+6+8+…+124
3)Find the number of terms of a geometric sequence with, first term1/64, common ratio 2, and last term 512
4)What is the coefficient of a^3 z^3 in the expansion of (a+z)^12
Click here to see answer by anantha(86)

Question 195625: What is the coefficient of a^3 z^3 in the expansion of (a+z)^12 : please i need help on these question can any one help me????
please help...
Click here to see answer by edjones(7569)

Question 195623: Write the following series in summation notation. Use i as index variable and start I at 1 2+4+6+8+…+124
please i need help on it please help
Click here to see answer by user_dude2008(1861)

Question 195833: Given the following sequence in geometric, find the common ratio and find the 10 th term:

please i need help please urgent!!!!!!!!!
i have exam on this question please.....
Click here to see answer by user_dude2008(1861)

Question 195832: find the mean of the 15 th through 55 th terms inclusive of the sequence:
a billow n = 7 - 4n please i need help to solve any one please help.....
Click here to see answer by RAY100(1637)

Question 195831: find the number of terms of a geometric sequence with, first term 1/64, common ratio 2 and the last term 512
please i need help please help.....
Click here to see answer by RAY100(1637)

Question 196057: Uncle Bob's will states you will recieve $1000 on your 21st birthday. Then every month afterward you will recieve 95% of the amount you recieved the previous month. When will you recieve an amount less than 1 cent? (which month after birthday) What will be the total you have recieved?
Click here to see answer by solver91311(16897)

Question 196139: I am trying to find the explicit formula for the following sequence:
-2 1/2, -2, -1 1/2, -1, -1/2
In this problem, -2 1/2 corresponds to the term 1, -2 corresponds to the term 2, -1 1/2 corresponds to the term 3, and so on. I've been working on this problem for over an hour and have tried lots of different formulas, but none work. Please help.
Thank you so much.
Click here to see answer by Earlsdon(6287)

Question 196326: Barbara has nickels, dimes, and quarters, worth $2.35 in her purse. The number of dimes is three less then sum of the numbers of nickels and quarters. How many of each type of coin does she have if there are 19 coins in all.
How would I even began to solve this? the chapter is about system of eyations with three variables, so there's a clue.
Click here to see answer by solver91311(16897)

Question 196389: The sum of any two prime numbers is divisible by 2?
Click here to see answer by Alan3354(30993)

Question 196447: In exercises 1-6, construct a difference table to predict the next term of each sequence.
4.) 0, 10, 24, 56, 112, 190
Click here to see answer by RAY100(1637)

Question 196526: Please help me solve this problem.
It says, Decide whether each infinite geometric series diverges or converges. State whether each series has a sum.
I understand that it diverges when the absolute value of r is > or = 1 and converges when the absolute value of r is < 1, but how do you know whether each series has a sum. For example one problem says:
1. 4 + 2 + 1 + ...
and I know that r=2 therefore it diverges but I can not figure out whether it has a sum or not.
Thanks for your time.
Click here to see answer by jim_thompson5910(28598)

Question 196817: Find the missing term of each geometric sequence?
26. 16, [?] , 4
27. 25, [?] , 225
28. 2, [?] , 50

Click here to see answer by Mathtut(3670)

Question 196818: Find the missing term of each geometric sequence?

29. 1, [?] , 49
30. 3/4, [?] , 3
31. 36, [?] , 4

Click here to see answer by user_dude2008(1861)

Question 196815:
Click here to see answer by Homework!Help!(1)

Question 196909: Determine whether each sequence is arithmetic or geometric. Then identify the common difference or the common ratio.
14. 1854, 1788, 1722, 1656, 1590, . . .
this is an arithmetic Progression
Common Difference = -66
15. 18, 45, 112.5, 281.25, 703.125, . . .
is a Geometric Progression
Common ratio = 2.5

16. 1, -4, 16, -64, 256, . . .
Geometric Progression
Common ratio = -4
17. -125, -108, -91, -74, -57, . . .
Arithmetic Progression
Common Difference = 17

Click here to see answer by mathsteacher(28)

Question 196908: Find the sum of each infinite geometric series

35. 4 -2 + 1 -1/2+...
common ratio = -1/2
Sn = a/(1-r)
= 4/(1--1/2)
= 4x2/3 = 8/3=2.66...
36. -13 1/2 + 9- 6+...
-13.5/(1+(2/3))
= 81/10 = 8.1
37. -5 -5/2 -5/2-...
-5/(1-1/2) = -10
Click here to see answer by mathsteacher(28)

Question 196907: Find the sum of each infinite geometric series.

32. 30 + 22.5 + 16.875 + . . .
Sn=a/(1-r)
r = 0.75
a = 30
Sn = 120
33. 15 - 3 + 0.6 - 0.12 + . . .
r = -0.2
a = 15
Sn = 12.5
34. 12 + 6 + 3 + . . .
a = 12
r = 0.5
Sn = 24

Click here to see answer by mathsteacher(28)

Question 197004: John invested $7000 for one year. He invested part of it at 8% and the rest at 12%. At the end of the year he earned $764 in interest. How much did he invest at each rate?
Click here to see answer by Mathtut(3670)

Question 196951: Find the arithmetic mean an of the given terms.
1. an-1=0,an+1=5
2. an-1=2/3,an+1=4
Click here to see answer by stanbon(57407)

Question 196965: Given each set of axes, what does the area under the curve represent?
48. y-axis: feet per second^2; x-axis: seconds
49. y-axis: dollars per pound; x-axis: pounds
50. y-axis: calories per ounce; x-axis: ounces
Click here to see answer by RAY100(1637)

Question 197716: sum[n-3,6,1/2n]
A - 19/2
B - 9
C - 6
D - 12
I reread my textbook and have tried trial-and-error and the process of elimination.
Click here to see answer by user_dude2008(1861)

Question 198172: This is from a worksheet from K12-OHVA- My internet school.
How do I find the sum of this finite geometric series? I will use an E for the Sigma notation.
8
E <-1/2)^i-1
i=1

Thank you
Click here to see answer by stanbon(57407)

Question 198207: Worksheet from my school OHVA
Find the sum of the arithmetic series
1+14+27+...+183
Thank you!
Click here to see answer by arallie(162)

Question 198323: Worksheet from school
Find the explicit and recrusive formula for the sequence:
10, 15, 20, 25, 30,...
and
1,4,9,16,25,36,49,...
Click here to see answer by user_dude2008(1861)

Question 198208: For questions 1-6 determine whether each series is arithmetic or geometric. Then evaluate the series to the given term.
1. 1+4+7+...; S8
2. 1+4+16+...; S8
3. 288+144+72+...; S7
4. 42+55+68+...; S12
5. -20-12-4+4+...; S10
6. 2-6+18-54+...; S10

Click here to see answer by arallie(162)

Question 198321: Worksheet from school-OHVA
Find the explicit formula for the following sequences:
123, 116, 109, 102, 95,...
and
1/6, 1/12, 1/24, 1/48, 1/96,...
Click here to see answer by user_dude2008(1861)

Question 198372: the product (1- 1/2)(1- 1/3)(1- 1/4) (1-1/5)…(1-1/99)(1-1/100) is equal to
a) 1/99 b) 1/80 c) 1/90 d) 1/100 e) none of these

Click here to see answer by jim_thompson5910(28598)

Question 198400: For questions 1-6 determine whether each series is arithmetic or geometric. Then evaluate the series to the given term.
4. 42+55+68+...; S12
5. -20-12-4+4+...; S10
6. 2-6+18-54+...; S10

Click here to see answer by arallie(162)

Question 198399: For questions 1-6 determine whether each series is arithmetic or geometric. Then evaluate the series to the given term.
4. 42+55+68+...; S12
5. -20-12-4+4+...; S10
6. 2-6+18-54+...; S10

Click here to see answer by arallie(162)

Question 198398:

For questions 1-6 determine whether each series is arithmetic or geometric. Then evaluate the series to the given term.
1. 1+4+7+...; S8
2. 1+4+16+...; S8
3. 288+144+72+...; S7

Click here to see answer by arallie(162)

Question 199031: addition of 1*1+2*2+3*3+......+50*50
Click here to see answer by solver91311(16897)

Question 199203: What is the equation to the problem twice the square of a number is the same as eight times the same number
Click here to see answer by Alan3354(30993)

Question 199680: Find the x values so that the infinite series become finite.
(infinite)
(Sigma) 3(x-2)^(k-1)
(k=1)
Could you help me with this question? Thank you.
Click here to see answer by jim_thompson5910(28598)

Question 199771: Hello and Thank You for your help.
I know the answewr to my problem is 10 years. I kept subtracting to get the answer. I don't know how to write an equation to solve the problem. The question is
Bill will put aside $100 per month this year for retiremenmt. Next year he will put away $200 per month the third year $300 per month. Each year will increase by $100 per month. How many years will Bill save to reach $66,000?
Click here to see answer by jim_thompson5910(28598)

Question 199910: the sum of a series with a set of 1+5+10+25+50
Click here to see answer by jim_thompson5910(28598)

Question 199930: I want to know the difference between a sequence and a progression. Are these two different from a pattern? Can you cite some examples. Is 1,11,111,1111,.... a sequence or a pattern. Are all sequences patterns or it is the other way.Similarly are all sequences progressions or it is the other way.
Click here to see answer by Edwin McCravy(8912)

Question 200754: state the next number in the sequence 1,1,1,2,2,3,3,4,5,5,8,6,13,7,21,8,34,9,_
Click here to see answer by jim_thompson5910(28598)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645