Search any question & find its solution
Question:
Answered & Verified by Expert
If the first, second and last terms of an A.P. be $a, b, 2a$ respectively, then its sum will be
Options:
Solution:
1693 Upvotes
Verified Answer
The correct answer is:
$\frac{3 a b}{2(b-a)}$
We have first term $A=a \ldots(i)$
Second term $A+d=b \ldots(ii)$
and last term $I=2 a \ldots(iii)$
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).
Second term $A+d=b \ldots(ii)$
and last term $I=2 a \ldots(iii)$
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).
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.