Question

In a sequence of (4n + 1) terms the first (2n + 1) terms are in AP whose common difference is 2 and the last (2n + 1) terms are in GP whose common ratio is 0.5. If the middle terms of the AP and GP are equal then the middle term of the sequence is

(a)  (n.2^{n + 1})/(2ⁿ - 1)

(b)  (n.2^{n + 1})/(2ⁿ - 1)

(c)  n.2ⁿ 

(d) None of these 

Answer 1

Correct option (a)  (n.2^{n + 1})/(2ⁿ - 1)

Let the sequence is a, a + 2, a + 4, …, a + 4n,

Therefore, middle term is a + 4n