Question

What is the sum of the first seven terms of the geometric series 2 − 8 + 32 − . . . ?

Answer 1

Answer:

$S_7=6554$

Step-by-step explanation:

The given series is $2-8+32-...$

The first term of the sequence is

$a_1=2$

There is a common ratio of

$r=-4$

The sum of the first n terms of a geometric sequence is given by the formula;

$S_n=\frac{a_1(1-r^n)}{1-r}$

We want to find the first seven terms so $n=7$

We substitute the given values into the formula to obtain;

$S_7=\frac{2(1-(-4)^7)}{1--4}$

$S_7=\frac{2(1--16384)}{1--4}$

$S_7=\frac{2(16385)}{5}$

$S_7=2(3277)$

$S_7=6554$

The correct answer is A