Question

The first five terms in a quadratic sequence are shown below.
6, 21, 46, 81, 126,...

What is the nth term in the sequence?

A. n2 + 5
B. 5n2 + 1
C. 6n2 + 1
D. 5n2 + 2

Answer 1

If we look at B
\[
n = 1 \implies 5 \cdot 1^2 + 1 = 6 \\
n = 2 \implies 5 \cdot 2^2 + 1 = 5 \cdot 4 + 1 = 21\\
n = 3 \implies 5 \cdot 3^2 + 1 = 5 \cdot 9 + 1 = 46\\
n = 4 \implies 5 \cdot 4^2 + 1 = 5 \cdot 16 + 1 = 81\\
n = 5 \implies 5 \cdot 5^2 + 1 = 5 \cdot 25 + 1 = 126\\
\]

Answer 2

Thanks! it was correct.