If the first, second and last term of an A.P. are a, b and 2a respecti

1.	If the first, second and last term of an A.P. are a, b and 2a respectively, its sum isA. \(\frac{ab}{2(b -a)}\)B . \(\frac{ab}{b-a}\)C. \(\frac{3ab}{2(b-a)}\)D. none of these
Answer» 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} = \(\frac{b}{2(b-a)}\{3a\}\) = \(\frac{3ab}{2(b -a)}\)

If the first, second and last term of an A.P. are a, b and 2a respectively, its sum isA. \(\frac{ab}{2(b -a)}\)B . \(\frac{ab}{b-a}\)C. \(\frac{3ab}{2(b-a)}\)D. none of these

Answer»

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}

= \(\frac{b}{2(b-a)}\{3a\}\)

= \(\frac{3ab}{2(b -a)}\)