Question

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

$7, 4, 1, -2$….

Short answer

The nth term of the sequence is $a_n=10-3n$.

Step-by-step solution

Step 1.  Given

The given sequence is 7, 4, 1, -2….

Step 2.  To determine

We have to find thenth term of the sequence.

Step 3.  Calculation

The given sequence 7, 4, 1, -2…. is an arithmetic sequence with common difference

$d=\text{2nd} \text{term}-1\text{st} \text{term}=4-7=-3$.

First term is $a_1=7$.

Using the term formula for arithmetic sequence we get:

$\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ =7+\left(n-1\right)\left(-3\right)\\ =7-3n+3\\ =10-3n\end{array}$

Hence, the nth term of the sequence is $a_n=10-3n$.