Question

the first term and the common difference of an A.P. is 0 and 10 respectively. Find the sum of first 25 terms of the A.P.​

Answer 1

S25=3000 and explanation in image

Answer 2

The sum of first 25 terms of the A.P.​($S_{25}$) = 3000

Step-by-step explanation:

Here, first term (a) = 0, common difference(d) = 10 and n = 25

To find,  the sum of first 25 terms of the A.P.​($S_{25}$)  = ?

We know that,

The sum of nth term of an AP

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

The sum of first 25 terms of the A.P.

∴ $S_{25} =\dfrac{25}{2} [2(0)+(25-1)10]$

⇒ $S_{25} =\dfrac{25}{2} [0+(24)10]$

⇒ $S_{25} =\dfrac{25}{2} \times 240$

⇒ $S_{25} =25 \times 120=3000$

Thus, the sum of first 25 terms of the A.P.​($S_{25}$) = 3000