Question

Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20, ......

Activity :- Here, a = 12, d = `square`, n = 100, S₁₀₀ = ?

S_n = `"n"/2 [square + ("n" - 1)"d"]`

S₁₀₀ = `square/2 [24 + (100 - 1)"d"]`

= `50(24 + square)`

= `square`

= `square`

Answer 1

Here, a = 12, d = 14 - 12 = 2, n = 100, S₁₀₀ = ?

S_n = `"n"/2 [2"a" + ("n" - 1)"d"]`

S₁₀₀ = `100/2 [24 + (100 - 1)"d"]`

= 50[24 + 99(2)]

= 50(24 + 198)

= 50(222)

= 11100