SOLUTION: Find the sum of the geometric sequence −3, 15, −75, 375, … when there are 7 terms and select the correct answer below. the options are: A) -39,063 B) 39,063 C) 58,593

Algebra ->  College  -> Linear Algebra -> SOLUTION: Find the sum of the geometric sequence −3, 15, −75, 375, … when there are 7 terms and select the correct answer below. the options are: A) -39,063 B) 39,063 C) 58,593       Log On


   

Question 1154282: Find the sum of the geometric sequence −3, 15, −75, 375, … when there are 7 terms and select the correct answer below.
the options are:
A) -39,063
B) 39,063
C) 58,593
D) -58,593
if you can, please include a thorough explanation!!! thanks!
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

first we need nth term formula:
write given terms as follow:
-3=3%2A%28-1%29%5E1%2A5%5E0
15=3%2A%28-1%29%5E%282%29%2A5%5E1
+-75=3%2A%28-1%29%5E3%2A5%5E2
375=3%2A%28-1%29%5E4%2A5%5E3
:
in general
3+%28-1%29%5En+%2A5%5E%28n+-+1%29
5th term
3+%28-1%29%5E5+%2A5%5E%285+-+1%29=3+%28-1%29%5E5+%2A5%5E4=-1875
6th term
3+%28-1%29%5E6+%2A5%5E%286+-+1%29=3+%28-1%29%5E6+%2A5%5E5=9375
7th term
3+%28-1%29%5E7+%2A5%5E%287+-+1%29=3+%28-1%29%5E7+%2A5%5E6=-46875

the sum of the first 7 terms geometric sequence is:
+-3%2B+15+-75%2B375-1875%2B9375-46875=-39063


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Find the sum of the geometric sequence −3, 15, −75, 375, … when there are 7 terms and select the correct answer below.
the options are:
A) -39,063
B) 39,063
C) 58,593
D) -58,593
if you can, please include a thorough explanation!!! thanks!
Use the formula for the sum of a GP: matrix%281%2C3%2C+S%5Bn%5D%2C+%22=%22%2C+a%5B1%5D%281+-+r%5En%29%2F%281+-+r%29%29

matrix%281%2C3%2C+S%5B7%5D%2C+%22=%22%2C+%28-+3%281+-+%28-+5%29%5E7%29%29%2F%281+-+-+5%29%29 ---- Substituting matrix%283%2C3%2C+7%2C+for%2C+n%2C+-+3%2C+for%2C+a%5B1%5D%2C+-+5%2C+for%2C+r%29 

 

matrix%281%2C3%2C+S%5B7%5D%2C+%22=%22%2C+%28-+3%281+%2B+%2278%2C125%22%29%29%2F6%29 

matrix%281%2C3%2C+S%5B7%5D%2C+%22=%22%2C+%28-+3%28%2278%2C126%22%29%29%2F6%29 

Sum of the 7 GP terms, or: