Question

The first term of an AP is 5, the last term is 45 and the sum is 400. find the number of terms and the common difference.

Answer 1

Here is your answer :-

We know that,

Sⁿ = n/2 ( a + l )

Where,

Sⁿ = sum of n terms.
a = first term
l = last term.
n = number of terms.

A/q,

400 = n/2 ( 5 + 45 )

➡ 400 = n/2 ( 50 )

➡ 25n = 400

➡ n = 400/25

➡ n = 16.

So, numbers of in this AP is 16.

Hope it will help you !!!

Answer 2

a = 5
l = 45 
sum = 400
sum = n/2 (a +l)
400  = n/2 (5+45)
800  = 50n
 n     = 800/50
 n     = 16
 
 therefore no. of terms = 16 ------------------ANSWER