Question

What is the sum of the geometric sequence –4, 24, –144, … if there are 7 terms? A) 308,829 B) –159,964 C) –411,772 D) 119,973 .

Answer 1

Answer:

The sum is -159964.

Step-by-step explanation:

Since, the sum of a geometric sequence is,

$S_n=\frac{a(1-r^n)}{1-r}\text{ When } |r| < 1$

or $S_n=\frac{a(r^n-1)}{r-1}\text{ When } |r| > 1$

Where, a is the first term of the sequence,

r is the common ratio,

n is the number of terms,

Given, sequence,

–4, 24, –144, …....., up to 7 terms,

Thus, a = - 4

$r=\frac{24}{-4}=-6$

And, n = 7,

Since, |-6| > 1

Therefore, the sum of the given sequence is,

$S_7=\frac{-4((-6)^7-1)}{-6-1}$

$=\frac{-4(-279936-1)}{-7}$

$=-\frac{4\times 279937}{7}$

$=-\frac{1119748}{7}=-159964$

Answer 2

Sum of the geometric sequence:
S n = a * ( 1- r^n ) / ( 1 - r )
a = - 4 ( the 1st term of the sequence ),  r = - 6,  n = 7
S 7 = (- 4 ) * ( 1 - ( - 6 )^7 )  / 1 - ( - 6 ) = ( - 4 ) * 279937 / 7 = - 159,964
Answer: B )