# What is the sum of the first 7 terms of the series −4+8−16+32−…?

Progressions are the sequences that follow a definite pattern. The formula for sum or product of consecutive terms in a progression can be calculated depending on the pattern, and this way, we can save a lot of time.

## Answer: The sum of the first 7 terms of the series −4+8−16+32−… is −172.

Let's understand in detail.

**Explanation:**

The sequence is given: −4+8−16+32−…

Now, we notice that the sequence is a type of geometric progression with a common ratio of -2.

Hence, the sum of GP = a (r^{n} - 1) / r - 1; where r is the common ratio, a is the first term and n is the number of terms.

Here, we have a = -4, r = -2 and n = 7

Hence, substituting the values in the formula:

sum = -4 ((-2)^{7} - 1) / (-2 - 1)

= -4 (-128 - 1) / -3

= -172