Question

What is the sum of the geometric sequence −3, 18, −108, ... if there are 7 terms?

Answer 1

Given conditions ⇒

Number of the terms (n) =  7
First term (a) = -3
Common ratio = 18/-3 = -6 

Since, the common ratio < 1.
∴ Formula to calculate the sum of the G.P. will be given by the relation, 

$S_{n} = \frac{a(1 - r^n)}{1 - r}$
 = -3[1 - (-6)⁷]/[1 + 6]
 = -3[1 + 279936]/[7]
 = -3[279937]/[7]
 = -3 × 9991
 = -119973 


Hence, the sum of the 7 terms in the G.P. Series is -119973. 


Hope it helps.

Answer 2

Solution:-

given by:-

first term (a) = -3.
secound term (a2) = 18
common raito (r ) =
$\frac{a2}{a} = \frac{18}{ - 3} = - 6$

number of term(n) = 7

by formula Sum of geometric sequence

$Sn = \frac{a(1 - {r}^{n} )}{1 - r} \\ \\ S _{7} = \frac{( - 3)(1 - {( - 6)}^{7} )}{1 + 6} \\ \frac{ - 3(1 + 279,936)}{7} \\ s_{7} = \frac{ - 839,811}{7} \\ s_{7} = - 119,973 \:$
hence your right answer - 119,973.

■I HOPE ITS HELP■