Question

Which formula matches with the sequence 2, 12, 72, 432,...?

A) a_n = 2^(n+1)
B) a_n = 6^n
C) a_n = 4^n
D) a_n = n^2 + n

Answer 1

The formula that matches with the sequence 2, 12, 72, 432,... is a_n = 2^(n+1).

Therefore, the correct answer is: option A) a_n = 2^(n+1)

Step-by-step explanation:

To see that the expression matches the sequence, imagine taking (n - 1) from the last term and adding it to the first term.

This is equal to 2[1 + (n - 1) + 3 + ... + (2n - 3) + (2n - 1) - (n - 1)] = 2[n + 3 + ... + (2n - 3) + n].

Now, take (n - 3) from the penultimate term and add it to the second term to get 2[n + n + ... + n + n] = 2n².

Therefore, the formula that matches with the sequence 2, 12, 72, 432,... is a_n = 2n+1.