Question

The following sequence is a geometric sequence

17
,
51
,
153
,
459
,
1377
,
...
Find the sum of the first 13 terms of this sequence.

What is the common ratio for this sequence?
r
=


What is the index of the final term of this sum?
last index =


What is the sum?
Sum =

Answer 1

13,551,737

Explanation:

You want the sum of the first 13 terms of the geometric sequence with first term 17, and successive terms 51, 153, ....

Common ratio

The common ratio is found by dividing a sequence term by the one before it:

r = 51/17 = 3

The common ratio is 3.

Index

The index of the 13th term of the sequence is n = 13.

Sum

The sum of n terms of a geometric sequence with first term a1 and common ratio r is ...

Sn = a1·(r^n -1)/(r -1)

For a1 = 17, r = 3, and n = 13, the sum is ...

`S_(13)=17\cdot(3^(13)-1)/(3-1)=17\cdot(1594322)/(2)=\boxed{13,\!551,\!737}`