Question

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

Answer 1

We have,

a₂ = 3 + 2n

a₁ = 3+ 2 × 1 = 5

a₂ = 3 + 2 × 2 = 7

a₃ = 3 + 2 × 3 = 9 …… and so on.

List of numbers become 5, 7, 9, …

a₂ – a₁ = 7 – 5 = 2

a₃ – a₂ = 9 – 7 = 2

∵ a₂ – a₁ = a₃ – a₂

The sequence forms an AP.

Here, a = 5

d = a₂ – a₁ = 7 – 5 = 2

n = 24

We know that S_n = n/2[2a + (n – 1)d]

⇒ S₂₄ = 24/2 [2 × 5 + (24 – 1) × 2]

⇒ S₂₄= 12 [10 + 23 × 2]

⇒ S₂₄ = 12 [10 + 46]

⇒ S₂₄ = 12 × 56 = 672

Hence, the sum of first 24 terms of list of numbers = 672.