Question

If first term of an A.P is a, second term is b and last term is c , then show that the sum of all terms is (a+c) (b+c-29)/2(b-a)​

Answer 1

first term = a

second term = b

last term(l) = c

common difference = b-a

An = a+(n-1)d

c = a+(n-1)(b-a)

(c-a)/(b-a) = n-1

(c-a-b+a)/(b-a) = n

(c-b)/(b-a) = n

Sn = (n/2)(a+l)

= [(c-b)/2(b-a)](a+c)

so, Sn = [(a+c)(c-b)]/2(b-a)

hence proved.