Question

For the sequence 1, 7, 25, 79, 241, 727 … simple formula for {an} is ____________

(a) 3^n+1 – 2

(b) 3^n – 2

(c) (-3)^n + 4

(d) n^2 – 2

I had been asked this question in an interview.

This intriguing question originated from Sequences and Summations topic in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Right option is (b) 3^n – 2

To explain: The ratio of consecutive numbers is close to 3. Comparing these terms with the sequence of {3^n} which is 3, 9, 27 …. Comparing these terms with the corresponding terms of sequence {3^n} and the nth term is 2 less than the corresponding power of 3.