SOLUTION: Please help again, appreciate any and all help. 2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following: a) What is r, the ratio between 2 consecutive terms

Algebra ->  Sequences-and-series -> SOLUTION: Please help again, appreciate any and all help. 2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following: a) What is r, the ratio between 2 consecutive terms      Log On


   

Question 39348: Please help again, appreciate any and all help.
2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Show work in this space.



b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer: the sum of the first 10 terms is: Show work in this space.

c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer: Show work in this space
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Common ratio...the number you multiple a term by to generate the next term.

1*3 is 3
3*3 is 9
9*3 is 27

--> r is 3

b.
1st term of a GP = a
2nd term of a GP = ar
3rd term of a GP = +ar%5E2+ and so,
nth term of a GP = +ar%5E%28n-1%29+

So, 10th term is +%281%29%283%29%5E%2810-1%29+
+%283%29%5E%289%29+
19683

c. Sum of n terms = +%28a%28r%5En-1%29%29%2F%28r-1%29+
+%28%281%29%28%283%29%5E10-1%29%29%2F%283-1%29+
+%283%5E10-1%29%2F2+
+%2859049-1%29%2F2+
29524

jon.