Question

how many terms of the ap -7,-13 by 2,-6,-11 by 2-5...... are needed​

Answer 1

The AP is -6, -11/2, -5, …

It is an AP with the first term as -6 and the common ratio is 1/2.

Sn = -25 = (n/2)[2a + (n-1)d]

= (n/2)[-12 +(n-1)*(1/2)]

= (n/2)[-12–1/2 + (n/2)]

= (n/2)[-25/2 + (n/2)]

-25*4 = n[-25+n]

n^2–25n+100 = 0

(n-20)(n-5) = 0

n = 20 or 5.

So either 5 terms or 20 terms of the AP will add up to -25.