Question

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

$1,3,5,7,\mathrm{....}$

Short answer

The nth term of the sequence is$a_n=2n-1$.

Step-by-step solution

Step 1.  Given

The given sequence is 1, 3, 5, 7....

Step 2.  To determine

We have to find thenth term of the sequence.

Step 3.  Calculation

The given sequence 1, 3, 5, 7... is an arithmetic sequence with common difference $d=\text{2nd} \text{term-1st} \text{term}=2$.

First term is $a_1=1$.

Using the term formula for arithmetic sequence we get:

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

Hence, the nth term of the sequence is $a_n=2n-1$.