Question

Find the eighteenth term of a sequence where the fifth term is 12 and the common difference is seven.

Short answer

The eighteenth term of a sequence is$103$

Step-by-step solution

Step 1. Given information

The fifth term of the series is$12$

The common difference is$7$

We have to find the ${18}^{th}$term of the series.

Step 2. Find the first term 

We have,

$$\begin{gathered} a_5=12 \\ d=7 \\ n=5 \end{gathered}$$

Put these values in $a_n=a_1+(n-1)d$

role="math" localid="1645297666368" $$\begin{gathered} 12=a_1+(5-1)7 \\ 12=a_1+\left(4\right)7 \\ {a}_1=12-28 \\ {a}_1=-16 \end{gathered}$$

Step 3. Find the term

Put obtained value in $a_n=a_1+(n-1)d$

$$\begin{gathered} a_{18}=-16+(18-1)7 \\ {a}_{18}=-16+\left(17\right)7 \\ {a}_{18}=-16+119 \\ {a}_{18}=103 \end{gathered}$$