Answer :

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.


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