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 the 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.
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 (rn - 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