Question

nth term of a Sequence Find the nth term of a sequence whose first several terms are given.

$-2,3,8,\mathrm{13....}$

Short answer

The nth term of the sequence is$a_n=5n-7$.

Step-by-step solution

Step 1.  Given

The given sequence is -2, 3, 8, 13….

Step 2.  To determine

We have to find thenth term of the sequence.

Step 3.  Calculation

The given sequence -2, 3, 8, 13…. is an arithmetic sequence with common difference

$d=\text{2nd} \text{term}-1\text{st} \text{term}=3-(-2)=3+2=5$.

First term is $a_1=-2$.

Using the term formula for arithmetic sequence we get:

$\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ =-2+\left(n-1\right)\left(5\right)\\ =-2+5n-5\\ =5n-7\end{array}$

Hence, the nth term of the sequence is $a_n=5n-7$.