Question

The common difference of of an AP is -2 find its sum if it dirst term is 100 and last term is - p

Answer 1

Step-by-step explanation:

d = -2, a = 100, Tn = -p

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

Sn = -p/2{2×100+[(-p)-1)(-2)]}

Sn = -p/2{200+(2p+2)}

Sn = -p/2{2[100+p+1]}

Sn = -p/2×2[101+p]

Sn = -p(101+p)

Sn = -101p-p^2

Sn = p^2-101