Question

Find the sum of first 24 terms of the list of numbers whose nth term is
given by
a = 3 + 2n​

Answer 1

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.

Answer 2

Solution :

As an

= 3 + 2n,

so, a¹

= 3 + 2 = 5

a² = 3 + 2 × 2 = 7

a³ = 3 + 2 × 3 = 9

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

Here, 7 – 5 = 9 – 7 = 11 – 9 = 2 and so on.

So, it forms an AP with common difference d = 2.

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

Therefore, S24 = [ ]

× + − × = 12 10 46 [ + ] = 672

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