###
**If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is**

A. n(n – 2)
B. n(n + 2)
C. n(n + 1)
D. n(n – 1)
**Answer: Option B**

## Show Answer

Solution(By Apex Team)

$\begin{aligned}a_n&=2n+1\\
a_1&=2\times1+1=2+1=3\\
a_2&=2\times2+1=4+1=5\\
\therefore d&=a_2-a_1=5-3=2\\
\therefore S_n&=\frac{n}{2}[2a+(n-1)d]\\
&=\frac{n}{2}[2\times3+(n-1)\times2]\\
&=\frac{n}{2}[6+2n-2]\\
&=\frac{n}{2}[2n+4]\\
&=n[n+2]\end{aligned}$

## 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