Question

Find the seventeenth term of a sequence where the first term is $-21$and the common difference is two.

Short answer

The seventeenth term of a sequence is$11$

Step-by-step solution

Step 1. Given information

The first term of the series is $-21$

The common difference is $2$

We have to find the${17}^{th}$ term of the series.

Step 2. Using formula to find the term.

The general term of the arithmetic series with the first term $a_1$and common difference $d$is: $a_n=a_1+(n-1)d$

We have,$$\begin{gathered} n=17 \\ {a}_1=-21 \\ d=2 \end{gathered}$$

Step 3. Put the values to find the term

Put the obtained value in the formula:

$$\begin{gathered} a_n=a_1+(n-1)d \\ {a}_{17}=-21+(17-1)2 \\ {a}_{17}=-21+\left(16\right)2 \\ {a}_{17}=-21+32 \\ {a}_{17}=11 \end{gathered}$$