SOLUTION: What is the sum of the first 15 terms in the geometric sequence 2, 4, 8? sometimes i got 65534 and sometimes i got 65536, im doing something wrong lol

Algebra ->  Sequences-and-series -> SOLUTION: What is the sum of the first 15 terms in the geometric sequence 2, 4, 8? sometimes i got 65534 and sometimes i got 65536, im doing something wrong lol      Log On


   

Question 88472: What is the sum of the first 15 terms in the geometric sequence 2, 4, 8?
sometimes i got 65534 and sometimes i got 65536, im doing something wrong lol
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The answer is 65,534
.
The sum of the terms in a geometric sequence (S) is given by the equation:
.
S+=+a%281-r%5En%29%2F%281-r%29
.
in which a is the first term, r is the ratio between terms, and n is the number of terms.
In this problem a = 2, r = 2, and n = 15. Substituting these values into the equation
leads to:
.
S+=+2%281-2%5E15%29%2F%281-2%29
.
A calculator will tell you that 2^15 = 32,768. Substituting this into the equation results in:
.
S+=+2%281-32768%29%2F%281-2%29
.
Simplify the terms that are inside the parentheses to get:
.
S+=+2%28-32767%29%2F%28-1%29
.
Do the multiplication in the numerator:
.
S+=+-65534%2F-1
.
and the division by -1 results in:
.
S+=+65534
.
Hope this helps you see how to use the equation for the sum of the terms in a geometric
progression.