Question

The first term of AP is5, the last term is 45 and the sum is 400 find the number of terms and the common differences

Answer 1

No.of terms =16

Common difference is 8/3

Here is the solution

Answer 2

Answer:

n= 16

Step-by-step explanation:

Values of n = 16 and

Values of n = 16 and d = 8/3

Step-by-step explanation:

Let a , d , l are first term , common difference and last term of an A.P , respectively.

given ,

a = 5, l = 45

We know that,

l = a +(n-1)d

Substitute values of a and l , we get,

⇒45 = 5+(n-1)d

⇒ 45-5 = (n-1)d

⇒ (n-1)d=40 ----(1)

Sum on n terms = $\frac{n}{2}$ ( 2a +(n-1)d) or

Given,

Sn= 400

⇒ 400= $\frac{n}{2}( 5+ 45)$

⇒ 400= $\frac{n}{2} (50)$

⇒ 400= 25n

⇒ n= $\frac{400}{25}$

n= 16

Now ,

Substitute n=16 in equation (1), we get

(16-1)d = 40

⇒ 15d =40

d = 40/15

⇒ d = 8/3

Therefore,

Values of n = 16 and

d = 8/3