Question

The first term of an Arithmetic Progression (A.P.) is 5, the last term is 50 and their sum is 440. Find:

1. the number of terms 
2. common difference

Answer 1

Given:

first term a = 5 last term l = 50 and sum Sn = 440 S_n = 440

(a) Using the formula for the sum of an A.P.:

`Sn = n/2(a + l)`

`440 = n/2(5 + 50)`

`440 = (55n)/2`

n = `880/55` = 16

Therefore, the number of terms is 16.

(b) Using the formula for the nth term:

l = a + (n − 1)d

50 = 5 + (16 − 1)d

45 = 15d

d = 3

Hence, the common difference is 3.