Question

Determine the formula for the nth term of the following sequence: 6, 14, 22, 30, 38, 46, ...an = -8n2 - 2an = -8n - 2an = 8n - 2an = 8n2 - 2

Answer 1

The sequence is 6, 14, 22, 30, 38, 46.

As you can observe, the sequence is increasing by a difference of 8 because 6+8=14, 14+8=22, 22+8=30, and so on. We have to use the arithmetic sequence formula

$a_n=a_1+(n-1)\cdot d$

Where a1 = 6 and d = 8.

$\begin{gathered} a_n=6+(n-1)\cdot8 \\ a_n=6+8n-8 \\ a_n=8n-2 \end{gathered}$

Hence, the correct sequence is an = 8n-2.