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 131743:
Given the term, -80, and the common ratio, -0.5, write the first 5 terms of the geometric sequence.
I don't know why I'm having such trouble with these.
Thank you in advance.
Click here to see answer by checkley71(8403)

Question 131740: State the common ratio and determine the next three terms for the geometric sequence 2, -8, 32, -128
Common ratio = (-4)
Next three terms = 512, -2,048, 8,192
Thank you in advance.
Click here to see answer by checkley71(8403)

Question 132270: Find the number of sides of a polygon if the differences between any two consecutive interior angles of the polygon is 5(degree) and the smallest angle is 120(degree).
Click here to see answer by nycsharkman(136)

Question 132279: On excercise 30A, there are some questions I was confused about, the numbers were, 24, 26, 28 and 30. What we were supposed to do was to find the formula, then find the 10th, or 15th or 20th term. Can you help me? This is how the questions come out in the book. The question below is number 24.
24. 1st:5 2nd:14 3rd:27 4th:44 5th:65 State the 10th and 20th term.
Click here to see answer by stanbon(57377)

Question 132698: Please help me solve this problem:
Click here to see answer by josmiceli(9691)

Question 133104: Use inductive reasoning to predict the next TWO numbers in the sequence.
80, –40, 20, –10, 5, . . .
I can't figure out what the pattern is her necessarily.
i get that its -120 +60 -30 +15 but i don't get what comes next.
Help me out with this please.
Click here to see answer by jim_thompson5910(28595)

Question 134424: Find the smallest whole number that when divided by 5,7,9, and 11, respectively, gives remainders of 1,2,3,and 4.
Click here to see answer by stanbon(57377)

Question 134728: please help THANK YOU! (-3+i) +(46i)
Click here to see answer by vleith(2825)

Question 134757: i cant figure out these problems
27. 75 sigma n=21 (2n+5) i solved this problem using the formula Sn=n/2(a1+an) and i got 5454 when the answer in the back was 5555. what did i do wrong
31. d=5, n=16, an=72 find Sn for the sequence
how do you get a1
help me solve these plese
Click here to see answer by vleith(2825)

Question 135251: How do I write this serie using sigma notation?
1/2 + 2/3 + 3/4 + ... 99/100
Click here to see answer by Fombitz(13828)

Question 135970: Find two numbers whose sum is 20 and whose product is 96.
Click here to see answer by checkley77(12569)

Question 136767: -15+-3+9+21+33+45+57+69+81+96
Click here to see answer by checkley77(12569)

Question 136910: find the sum of the first 10 terms of the series 9+18+36+...
Click here to see answer by dolly(163)

Question 137056: Is there a short way to do the SUM of a sequence of sums: (1) + (1+2) + (1+2+3) + (1+2+3+4) + .... (1+2+3+4....+100). I know how to do the sum of the sequence (i.e. sum of 100= 100/2(100 + 1)) and I can get the answer, I am just trying to see if there is an easier way then adding each number up. Like, sum for 100 is 5050; sum of 99 is sum of 100 minus 100 or 4050; but I can't find a shortcut and I can't find a formula anywhere for the sum of a series of sums. Can someone help? This is actually not for a class.
Click here to see answer by solver91311(16897)

Question 137271: The difference of two numbers is 1. 1/7 the larger number less 1/9 the smaller number is 1. Find the numbers.
Click here to see answer by oscargut(891)

Question 137342: Find the sum of the first thirty terms of the following arithmetic series:
16+25+34+43...
Click here to see answer by stanbon(57377)

Question 137342: Find the sum of the first thirty terms of the following arithmetic series:
16+25+34+43...
Click here to see answer by Fombitz(13828)

Question 137345: Find the sum of the first fifteen terms of the geometric series:
2-3+4.5-6.75+10.125
Click here to see answer by stanbon(57377)

Question 137667: Evaluate.
For a certain arithmetic series, S4=50 and S5=75. Find the first five terms.
I know the answer to this question is -25, 0, 25, 50, and 75, but I have to show my work and i'm not sure how i should do this. Can u help?
Thanx.
Click here to see answer by oscargut(891)

Question 139230: I am in 9th grade advanced algebra 2 and am stumped on 4 of my sequence problems. The other 11 made complete sense, so now I am getting uptight....
The sequences are as follows
0,3,7,12,18,.....
2,-2,-18,-52,-110,-198,.....
4,23,64,133,236,379,568,.....
-5,-9,-19,-35,-57,-85,....
Click here to see answer by checkley77(12569)

Question 139304: I need to find the geometric means in the sequence
180,____,5
and i need to know how to solve it
Click here to see answer by stanbon(57377)

Question 139370: the sum of two whole numbers is 72 the diffenence between them is 48 what is the number?

Click here to see answer by checkley77(12569)

Question 140298: The median of 5 natural numbers is 8, the mean of the set is 7 and the mode of the set is 10. What is the largest possible value that the range of the set can have?
Thankyou for your help. Danielle..
Click here to see answer by scott8148(6628)

Question 140430: In how many ways can three numbers be selected from the set {1,3,4,6,7,8,11} so that the sum of the three numbers is even? In how many ways can three numbers be selected so that their product is odd?
Would my first step be understanding that I need 2 even and 1 odd, or 3 odd to get odd and then 2 odds and 1 even and 3 even to get evens?
Thankyou Maria
Click here to see answer by stanbon(57377)

Question 140685: I had a question similar to this one earlier. This one is of a different format though. If Given A5= -5 and A9=10 find d and A1
Click here to see answer by stanbon(57377)

Question 140684: I am struggling with a couple of these types of problems. Not sure how to find results. My on-line instructions hasn't given me a good example.
If given A7 = 16 and A11= 256 Find r and A1? Thanks!
Click here to see answer by stanbon(57377)

Question 140683: I need to find the 20th partial sum of sequence 17,23,29,35... I have found d=6 and the 20th term is 131, but what next to find partial sum? Thank You
Click here to see answer by stanbon(57377)

Question 140761: I trying to find out how to acomplish this problem:
It states to: Find the X^7 term in the Expansion of (X+Y)^11
Click here to see answer by scott8148(6628)

Question 140811: I am asked to write a formula for the Nth term of:
2/3, 3/4, 4/5, 5/6 . What does my formula look like?
Click here to see answer by stanbon(57377)

Question 140835: Can someone help me calculate the 20th partial sum for 6400,1600,400,100,25...?
Click here to see answer by stanbon(57377)

Question 141049: write the first five terms of the sequence defined by the given recursive or explicit formula. t_n=32-8n
Click here to see answer by Edwin McCravy(8909)

Question 131727: I am doing a unit on geometric/arithmetic series and sequences.
Here is the problem:
Determine S25 for 3 + 3x2 + 3x4 + 3x6 + . . .
I know that this is a geometric series and a=3.
I know I will use the formula: S25 =(1-rn)/1-r,
but I cannot figure out what the r is?
Click here to see answer by stanbon(57377)

Question 141060: The 15th term of an arithmetic series is 52, and the sum of the first 15 terms is 405. Find the first term of the series.
This problem is from the Resource Book for McDougal Littell's Algebra 2 book -- The worksheet is called :Challenge: Skills and Applications, Lesson 11.2
Click here to see answer by Edwin McCravy(8909)

Question 141069: (a) Find x if the numbers 3-x, x, and 1-3x form an arithmetic sequence. And then (b) find the next term of the sequence after the ones represented in part (a).
Click here to see answer by stanbon(57377)

Question 141070: Show that if the sum of an arithmetic series with an odd number of terms is 0, then one of the terms of the series must be 0. (Hint: let the number of terms be 2k + 1. Show that a1 = -kd. Then find the (k + 1)st term.)
Click here to see answer by vleith(2825)

Question 141061: The 12th term of an arithmetic series is 42 and the sum of the first 17 terms is 51. Find the common difference of the series, and find the first three terms of the series.
Click here to see answer by stanbon(57377)

Question 141245: What number completes the pattern ?
10%, 11.11%, 12.5%, 14.28%, ___________, 20%

what i have tried:
.1111-.1000=.111
.1250-.1111=.139
.1428-.1250=.178

.178-.139=.39-.11=.139-.111=.28
.178+.11+.39=.228
and so on....not working !

Click here to see answer by scott8148(6628)

Question 141732: Q1.THE greatest term of series
2^1/2,3^1/3,4^1/4,.........,100^1/100 will be
Q2.Sum of the solution of the equation
2.8^x+32.8^-x=65
Click here to see answer by stanbon(57377)

Question 141826: directions....find the sum and product of the roots of each quadratic equation.
x^2+8x=-7
Click here to see answer by nabla(475)

Question 142025: The fourth term of a GP (Geometric Progression) is 56 while the sixth term is 7/8. Find the GP and hence S(infinity)...
Click here to see answer by stanbon(57377)

Question 142020: Find the value of the 50th term of the series: 180+162+145.8+131.22+...
Click here to see answer by stanbon(57377)

Question 142024: The sum of the first 12 terms of an AP (Arithmetic Progression) is 222, the sum of the first 5 terms is 40. Write out the first four terms of the series.
Click here to see answer by nabla(475)

Question 142143: Find the sum of the first 12 terms of the arithmetic series.
-5 + 0 + 5 +10 + ...
Click here to see answer by nabla(475)

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