Question

the first term of ap is 5 and the last term is 45 and yhe sum is 400 find the number of terms and the comman difference ​

Answer 1

Answer:

In an AP,

First term (a) = 5

Last term (l) = 45

Sum of the terms of the AP (Sn) = 400

Number of terms = (n) = ?

Common difference = (d) = ?

Now,

Sn = n/2 × (a + l)

=> 400 = n/2 × (5 + 45)

=> n/2 × 50 = 400

=> n = (400 × 2)/50

=> n = 16

Again,

l = a + (n - 1)d

=> 45 = 5 + (16 - 1) × d

=> 45 - 5 = 15d

=> d = 40/15 = 8/3