Find the sum of the geometric sequence −3, 15, −75, 375, ... when there are 7 terms and select the correct answer below. −39,063 39,063 58,593 −58,593
Accepted Solution
A:
ANSWER−39,063EXPLANATIONThe given geometric sequence is -3,15,-75,375,...The sum of the first n-terms of a geometric sequence is calculated using the formula;[tex]S_n = \frac{a(1 - {r}^{n}) }{1 - r} [/tex]Where a=-3 is the first term of the geometric sequence and [tex]r = \frac{15}{ - 3} = - 5[/tex]is the common ratio of the sequence.The sum of the first seven terms is [tex]S_7= \frac{ - 3(1 - {( - 5)}^{7}) }{1 - - 5} [/tex][tex]S_7= \frac{ - 3(1 + {( 5)}^{7}) }{6} [/tex]This simplifies to:[tex]S_7= - 39603[/tex]