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

A. $\frac{a b}{2(b-a)}$
B. $\frac{a b}{b-a}$
C. $\frac{3 a b}{2(b-a)}$
D. None of these
**Answer: Option C**

## Show Answer

Solution(By Apex Team)

First term ($\mathrm{a}_{1}$) = a
Second term ($\mathrm{a}_{2}$) = b
and last term (l) = 2a
∴ d = Second term – First term = b – a
$\begin{aligned}&\therefore l=a_n=a+(n-1)d\\
&\Rightarrow2a=a+(n-1)(b-a)\\
&\Rightarrow(n-1)(b-a)=a\\
&\Rightarrow n-1=\frac{a}{b-a}\\
&\Rightarrow n=\frac{a}{b-a}+1\\
&\Rightarrow n=\frac{a+b-a}{b-a}\\
&\Rightarrow n=\frac{b}{b-a}\\
\therefore S_n&=\frac{n}{2}[a+l]\\
&\quad=\frac{b}{2(b-a)}[a+2a]\\
&\quad=\frac{3ab}{2(b-a)}\end{aligned}$

## Related Questions On Progressions

### How many terms are there in 20, 25, 30 . . . . . . 140?

A. 22B. 25

C. 23

D. 24

### Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

A. 5B. 6

C. 4

D. 3

### Find the 15th term of the sequence 20, 15, 10 . . .

A. -45B. -55

C. -50

D. 0

### The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

A. 600B. 765

C. 640

D. 680