If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is A. ab /2(b-a)

Question

If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is

A. \(\frac{ab}{2(b -a)}\)

B . \(\frac{ab}{b-a}\)

C. \(\frac{3ab}{2(b-a)}\)

D. none of these

Answer 1

a, b and 2a are in A.P so a is the first term and 2a is the last term denoted by T and T_n respectively. Here Common difference = b – a 

T_n = 2a = a + (n–1) (b–a) 

So n = \(\frac{b}{b-a}\)

Sum = \(\frac{n}{2}\){first term + last term}

= \(\frac{b}{2(b-a)}\{3a\}\)

= \(\frac{3ab}{2(b -a)}\)