If the pth term of an A.P. is a and qth term is b, show that the sum of (p + q) terms
is
Let A be the first term and D be the common difference.
...(i)
...(ii)
Subtracting (ii) from (i), we get
(p - 1)D - (q - 1) D = a - b or (p - q)D = a - b
or ...(iii)
Adding (i) and (ii), we get
2A + (p - 1)D + (q - 1) D = a + b or 2A + (p - 1 + q - 1)D = a + b
or 2A + (p + q - 1)D - D = a + b (Note this step carefully)
or 2A + (p + q - 1)D = a + b + D
or 2A + (p + q - 1)D = a + b + { By using (iii)} ...(iv)
[By using (iv)]