Question

Find the twenty-fifth term of a sequence where the first term is five and the common difference is three.

Short answer

The twenty-fifth term of the series is$77$

Step-by-step solution

Step 1. Given information

The first term of the series is $5$

The common difference is $3$.

We have to find the${25}^{th}$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: localid="1645295885091" $a_n=a_1+(n-1)d$

Put $$\begin{gathered} n=25 \\ {a}_1=5 \\ d=3 \end{gathered}$$

Step 3. Put the values to find the term

Put the obtained value in the formula:

$$\begin{gathered} a_n=a_1+(n-1)d \\ {a}_{25}=5+(25-1)3 \\ {a}_{25}=5+\left(24\right)3 \\ {a}_{25}=5+72 \\ {a}_{25}=77 \end{gathered}$$