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`

Explanation

To prove that the sum of the first \( (p + q) \) terms of an arithmetic progression (A.P.) is given by

\[ S_{p+q} = \frac{(p + q)}{2} \left( a + b + \frac{(a - b)}{(p - q)} \right), \]

where the \( p^{th} \) term is \( a \) and the \( q^{th} \) term is \( b \), we can follow these steps:

...