Question

The first term of an AP is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The common difference of AP is 3.

Step-by-step explanation:

Let the common difference of AP is d.

First term of an AP is 2.

nth term of an AP is

$a_n=a+(n-1)d$

The last term is 50.

$50=2+(n-1)d$

$48=(n-1)d$                 .... (1)

Sum of n term of an AP is

$S_n=\frac{n}{2}[2a+(n-1)d]$

The sum of all these terms is 442.

$442=\frac{n}{2}[2(2)+(n-1)d]$

Using equation (1), we get

$442=\frac{n}{2}[4+48]$

$442=\frac{n}{2}(52)$

$442=26n$

$n=17$

The value of n is 17. Put this value in equation 1.

$48=(17-1)d$

$48=16d$

$d=3$

Therefore the common difference of AP is 3.