Question

The first term of an AP is 3, the last term is 83 and the sum of all its terms is 903. Find the number of terms and the common difference of the AP.

Answer 1

Given:
a = 3
l = 83

Sum all the n terms = 903
S_n = 903

`("n")/(2) [ "a" + "l"] = 903`

`("n")/(2). (3+83) = 903`

`"n". 43 = 903`

`"n" = (903)/(43)`

n = 21

Number of terms = 21

∵l = 83

a + (n - 1) d = 83

3 + (21 - 1) . d = 83

20d = 80

d = 4

∴ Common difference = 4
∴ n = 21 and d = 4