How many terms of the AP - 15, - 13, - 11, … are needed to make the sum - 55?

Let n number of terms are needed to make the sum - 55.

Here, first term , a = - 15

common difference, d = - 13 + 15 = 2

By using the sum of n terms formula,

- 110 = n (- 30 + 2n - 2)

- 110 = n(2n - 32)

2n² - 32n + 110 = 0

n² - 16n + 55 = 0

n² - 11n - 5n + 55 = 0

n(n - 11) - 5(n - 11) = 0

(n - 5)(n - 11) = 0

So n is either 5 or 11

Hence, either 5 and 11 terms are needed to make the sum - 55.