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 = \[\boxed{2}\], n = 100, S₁₀₀ = ?

S_n = \[\frac{\text{n}}{2} [\boxed{\text{2a}} + (\text{n} - 1)\text{d}]\]

S₁₀₀ = \[\frac{\boxed{100}}{2} [24 + (100 - 1)\text{d}]\]

= 50[24 + 99(2)]

= \[50(24 + \boxed{198})\]

= \[\boxed{50(222)}\]

= \[\boxed{11100}\]