Question

If the sum of first n terms of an AP is given by Sn = 4n^2 + 6, then its first term will be _________

(a) 4

(b) 3

(c) 5

(d) 1

The question was posed to me in a national level competition.

My query is from Sum of N Terms of Arithmetic Progression topic in division Arithmetic Progressions of Mathematics – Class 10

Answer 1

Correct choice is (a) 4

The explanation: The sum of first n terms of an AP is given by Sn = 4n^2 + 6.

Substituting n by n – 1 in the given equation

Sn – 1 = 4(n – 1)^2 + 6

Sn – 1 = 4n^2 – 8n + 4 + 6

Sn – 1 = 4n^2 – 8n + 10

∴ Tn = Sn – Sn – 1

Tn = 4n^2 + 6 – (4n^2 – 8n + 10)

Tn = 8n – 4

The first term will be T1 = 8(1) – 4 = 4