Question

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

• A. (nx2ⁿ⁺¹)/(2ⁿ-1)
• B.
• C. nx2ⁿ
• D. n²-n

Answer 1

The correct option is A (nx2ⁿ⁺¹)/(2ⁿ-1)

Assumption

At n=1, there are 5 terms in this sequence. The $2^{nd}$ and the $5^{th}$ term are equal. One such sequence which satisfies the given conditions is 02421.

Based on this, the middle term is 4

Look in the answer options for a value 4, on substitution of n=1. Answer is option (a)