Question

The `p^(t h)` term of an A.P. is `a` and `q^(t h)` term is `b` Prove that the sum of its `(p+q)` terms is `(p+q)/2{a+b+(a-b)/(p-q)}dot`

Answer 1

`a_1+(p-1)d=a-(1)`
`a_1+(q-1)d=b-(2)`
subtracting equation 2 from 1
`a_1+pd-d-a_!-qd+d=a-b`
`(p-q)d=a-b`
`d=(a-b)/(p-q)`
Sum of p+q terms
`S=(p+q)/2[2a+(p+q-1)d]`
`S=(p+q)/2[a+b+d]`
`S=(p+q)/2[a+b+(a-b)/(p-q)]`.