Question

(i) n^th term of some sequence are given below. Which term can be the n^th term of an AP?

(a) a_n = n(n + 1)

(b) a_n = 2 + 5n

(c) a_n = 2ⁿ + 2

(d) a_n = n² + n + 1

(ii) If the sum of 12^th and 22^nd terms of an AP is 100. Find the sum of first 33 terms. 

Answer 1

(i) (b) a_n = 2 + 5n.

(ii) t₁₂ + t₂₂ = 100 

⇒ a + 11d + a + 21d = 100

⇒ 2a + 32d = 100

S₃₃ = \(\frac{33}{2} (2a + 32d) = \frac{33}{2} \times 100 = 1650\)