If the first, second and the last terms of an A.P. are a,b,c respectively, then the sum of the A.P. is

Options

A. `((a+b)(a+c-2b))/(2(b-a))`
B. `((b+c)(a+b-2c))/(2(b-a))`
C. `((a+c)(b+c-2a))/(2(b-a))`
D. none of these

Answer

C

Explanation

Let there be n terms in the A.P. Then,
`c=a+(n-1)(b-a)" "[becaused=b-a]`
`rArrn=(b+c-2a)/(b-a)`
`:." Sum of n terms"=(n)/(2)(a+c)=((b+c-2a)(a+c))/(2(b-a))`