Question

What is the sum of the geometric sequence −1, 6, −36, ... if there are 7 terms?

Answer 1

HELLO DEAR,

GIVEN g.p. is -1 , 6 , -36 , ....... 7th terms.

so, a₁ = -1 , r = 6/-1 = -6

we know the foumula for $\sf{S_n = \frac{a(r^n - 1)}{r - 1}}$

$\sf{S_7 = \frac{(-1)[(-6)^7 - 1]}{-6 - 1}}$

$\sf{S_7 = \frac{(-1)[-279936 - 1]}{-7}}$

$\sf{S_7 = \frac{279937}{-8}}$

$\sf{S_7 = -39991}$


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Dear Student,

Solution:

Given sequence is -1, 6, - 36,...

By analysis we can judge that it is a GP

here first term a = -1

Common ratio r = 6/-1 = -6

number of terms n = 7

Sum of n terms in GP =
$\frac{a(1 - {r}^{n} )}{1 - r} \: \: \: \: \: \: r < 1 \\ \\ = \frac{ - 1(1 - ( { - 6)}^{7} )}{(1 - ( - 6))} \\ \\ = \frac{ - 1(1 + 279936)}{7} \\ = - 39991$
Is the answer.

Hopefully this helps you.