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 326186: Please help me solve this...
The first term of a geometric sequence is 12, and the second term is 3, find the 5th term.
Click here to see answer by Fombitz(13828)

Question 326423: An=3n-1
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Question 326512: the sum of the 1st and 2nd term of a geometric progression is 10 while its sum to infinity is 18. find the fourth term
Click here to see answer by galactus(183)

Question 326766: There is a very famous sequence of numbers called Fibonacci Numbers. Here are the first eight: 1 1 2 3 5 8 13 21. What is the tenth Fibonacci number?
A.55
B.89
C.123
D.113
E.144

Click here to see answer by mananth(12270)

Question 327097: list all the two-digit numbers which leave a remainder of 6 and when 171 is divided by them
Click here to see answer by Fombitz(13828)

Question 291148: Find the 100th term and the nth term for each of the following sequences.
a) 1, 3, 5, 7, 9
b) 0, 50, 100, 150, 200
c) 3, 6, 12, 24, 48
d) 10, 100, 1,000, 10,000, 100,000 (write in scientific notation or mention how many 0’s are in the number)
e) 9, 13, 17, 21, 25, 29
f) 1, 8, 27, 64, 125

Click here to see answer by brooks(2)

Question 328453: find the sum of the series 5/13 + 55/(13)^2 + 555/(13)^3 + ...
Click here to see answer by galactus(183)

Question 328502: In the expansion of (1 + 1/6x) to the power n, n belongs to N, n>8 the coeffient of x to the power 7 and x to the power 8 are equal find n.
I have tried n(n-1)....(n-6) (1) to the power n-7 all over 7!
and n(n-1)....(n-7)(1) to the power n-8 all over 8!
1 = n-7 over 8
8 = n-7
n=15

Click here to see answer by Fombitz(13828)

Question 328501: I need to find the sum of the first n terms of the g.p. 4,12,36... and find the least value of n for which the sum is greater than 500,000.
I know that
r = 3 and a = 4 but then I am stuck.
Click here to see answer by josmiceli(9681)

Question 328497: In an arithmetric progression the sum of the first 8 terms is 54 and the 6th term is 3 times the second term. I need to find the first term and the sum of the first 20 terms.
I have been over this question so many times any help would be gratefull thanks.
Click here to see answer by scott8148(6628)

Question 328689: I need to show that 11! has a remainder of 1 when divided by 13 without the use of a calculator any ideas please.
Click here to see answer by galactus(183)

Question 328651: r=1/3 A1=4
Click here to see answer by Fombitz(13828)

Question 328803: If n is any integer, then 2n is an even integer and 2n + 1 is an odd integer. Consecutive integers are one right after each other. If n is any integer, then n + 1 would be the next integer and n + 2 would be the next integer and so on.
a.) Find two consecutive odd integers such that the sum of their reciprocals is the fraction 12 over 35

Click here to see answer by Fombitz(13828)

Question 329452: If I adding odd numbers from -7 to 101. Can you show me how to get the sum the quickest way possible?
Click here to see answer by stanbon(57361)

Question 329961: $38,250 + $80,000+ $22,250-0.25($80,000 + $38,250) =
Click here to see answer by checkley77(12569)

Question 330097: The third term of a geometric sequence is 32 and the fifth term is 512. What is the eighth term of the sequence?
Click here to see answer by Fombitz(13828)

Question 330195: Find three consecutive multiples of 5 such that the sum of the squares of the first two is 125 greater than the square of the third.
This is what I did, but it's wrong.

25N + 25N + 25 - 125 = 25N + 100
25N - 100 = 100
25N = 200
N = 8
Click here to see answer by Alan3354(30993)

Question 331346: The third and fourth terms of a sequence are 26 and 40. If the second differences are a constant 4, what are the first five terms of the sequence?

Click here to see answer by Edwin McCravy(8909)

Question 331281: If a geometric sequence starts with a first term of 2 and grows exponentially by a factor of 3, what is the sum of the 4th and 5th terms?
(a) 216 (b) 162 (c) 108 (d) 54 (e) 27
Click here to see answer by Edwin McCravy(8909)

Question 331422: how do I solve this problem
"find the 8th term in the expansion of (2c-3d)^14
Click here to see answer by Edwin McCravy(8909)

Question 331661: the summation of -3 times 5/6 to i - 1 power as i goes from 1 to 5
Click here to see answer by solver91311(16897)

Question 331955: Scientific notation is most effective when used with a. very small numbers, b. Very large numbers, c. Imaginary numbers or d. very large and very small numbers.
Click here to see answer by Alan3354(30993)

Question 332819: infinity
E 6(.02)^i
i=1
Click here to see answer by galactus(183)

Question 332996: if interest is compounded annually, how long does it take $1,000 to double at 8% interest?
Click here to see answer by mananth(12270)

Question 334426: Can you show me how to write in decimal notation 2.34 x 10^6 Thank you
Click here to see answer by Alan3354(30993)

Question 334467: please provide the next number is sequence 4, 32, 2048
thank you in advance
Click here to see answer by Fombitz(13828)

Question 332881: find the first five terms of a1=3, aN=aN-1+2(n-2), n>or=2
Click here to see answer by Edwin McCravy(8909)

Question 335383: I have a triangle of dots progressing in size. The first triangle has one dot, the second triangle has three dots, the third triangle has nine dots, ect. I need help with the formula when it asks how many dots the "nth" triangle has.
Click here to see answer by Edwin McCravy(8909)

Question 335387: What is the series with summation notation of the following fractions: thank you so much!
Click here to see answer by Edwin McCravy(8909)

Question 335634: Alfred is practicing typing. The first time he tested himself, he could type 23 words per minute. After practicing for a week, he could type 26 words per minute. After two weeks he could type 29 words per minute. Based on this pattern, predict how fast Alfred will be able to type after 4 weeks of practice
Click here to see answer by stanbon(57361)

Question 336210: An auditorium has 20 rows of seats.These are 20 seats in the first row,21 in the second row and 22 in the third row and so on.how many seats are there in all rows?
Click here to see answer by galactus(183)

Question 336304: a G.P has a first term of a, a common ratio of r and its 6th term is 768. another G.P has a first term of a, a common ratio of 6r and its 3rd term is 3456. evaluate a and r.
Click here to see answer by galactus(183)

Question 336393: find a formula for 43, 41, 39, 37, 35
Click here to see answer by user_dude2008(1861)

Question 336429: I need to find the 100th term, for the sequence 2,6,12,20
Click here to see answer by Edwin McCravy(8909)

Question 336461: fill in the blank with one of the digits from 1 through 9 (using each digit only once) to make a true statement. using the following functions / then x then+ then x then x then / then + then x that = 100 (___ / ___ x ___ + ___ x ___ x ___ / ___ + ___ x ___ =100)

Click here to see answer by Edwin McCravy(8909)

Question 336658: what is the sequence of 6, 12, 9, 18, 15?
Click here to see answer by Edwin McCravy(8909)

Question 336706: find the sum of each of the following infinite seies.if a series does not have a sum write no sum as the answer
1) 1/2+1+2+4
2)9-3+1-1/3+1/9
Click here to see answer by Fombitz(13828)

Question 336724: find the missing numbers to complete the pattern
1,2,_, _, _, 32
Click here to see answer by Fombitz(13828)

Question 336724: find the missing numbers to complete the pattern
1,2,_, _, _, 32
Click here to see answer by jim_thompson5910(28595)

Question 336715: a. 1, 3, 5, 7, 9
b. 0, 50, 100, 150, 200
c. 3, 6, 12, 24, 48
d. 10, 100, 1,000, 10,000, 100,000
e. 9, 13, 17, 21, 25, 29
f. 1, 8, 27, 64, 125
Find the 100th term and the nth term for each of the
sequences in exercise 2.
Click here to see answer by Edwin McCravy(8909)

Question 337512: Can you help me find the following 3 numbers:
1, 5, 14, 30, 55 ___ ___ ___?
Click here to see answer by Fombitz(13828)

Question 337511: Can you help me find the following next 3 numbers:
1, 1, 2, 3, 5, ___ ____ ___ ?
Click here to see answer by solver91311(16897)

Question 337388: For the pattern shown below, describe a rule for finding the next term. Then use your rule to write the next 3 terms....

-2, -8/5, -6/5, -4/5,... the next one is -2/5 I'm not sure about the next two. I'm thinking the next one is -1 but not sure at all. Thank you.
Click here to see answer by mananth(12270)

Question 338482: write an equation for the following sequence:
0, 10, 15, 17.5 18.75

Click here to see answer by fractalier(2101)

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