Question

If the first, second and last terms of an A.P. be $a , b , 2 a$ respectively, then its sum will be.

• A. $\frac { a b } { b - a }$
• B. $\frac { a b } { 2 ( b - a ) }$
• C. $\frac { 3 a b } { 2 ( b - a ) }$
• D. $\frac { 3 a b } { 4 ( b - a ) }$

Answer 1

Answer: (C)

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

Answer 2

We have first term $A = a$ ......(i)

Second term $A + d = b$ ......(ii)

and last term $l = 2 a$ ......(iii)

From (i), (ii) and (iii), $d = ( b - a )$ and $n = \frac { b } { b - a }$

Then sum $S = \frac { n } { 2 } [ a + l ] = \frac { b } { 2 ( b - a ) } [ a + 2 a ] = \frac { 3 a b } { 2 ( b - a ) }$

Trick : Let $a = 2 , b = 3$ then the sum $= 9$ which is given by option (3).