Question

Find the sum of first 24 terms of the list of numbers whose n^th term is given by a_n = 3 + 2n.

Answer 1

a_n = 3 + 2n 

a₁ = 3 + 2 = 5 

a₂ = 3 + 2 x 2 = 7 

a₃ = 3 + 2 x 3 = 9 

List of numbers becomes 5, 7, 9. 11, …

Here,7 – 5 = 9 – 7 = 11 – 9 = 2 and soon. So, it forms an A.P. with common difference d = 2. 

To find S₂₄, we have n = 24, a = 5, d = 2.

S₂₄ = (24/2) [2 x 5 + (24 – 1) x 2] 

= 12 [10 + 46] = 672 

So, sum of first 24 terms of the list of numbers is 672.