Question

An arithmetic sequence is as follows: 2, 24, 46... find the formula for the nth term.

Answer 1

The nth term of an arithmetic sequence is given as:

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

Where

a_1 is first term

d is common difference (diff between terms)

n is the term number

Now,

in the sequence, we see

First Term = 2

Common DIff = 24 - 2 = 22 and 46 - 24 = 22, so Common Difference = 22

So, the general formula is:

$\begin{gathered} a_n=a_1+(n-1)d \\ a_n=2+(n-1)(22) \\ a_n=2+22n-22 \\ a_n=22n-20 \end{gathered}$