Question

Find the thirtieth term of a sequence where the first term is $16$ and the common difference is $-5$.

Short answer

The thirtieth term of a sequence is$-44$

Step-by-step solution

Step 1. Given information

The first term of the series is $16$

The common difference is $-5$

We have to find the${13}^{th}$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: role="math" localid="1645296479868" $a_n=a_1+(n-1)d$

We have,$$\begin{gathered} n=13 \\ {a}_1=16 \\ d=-5 \end{gathered}$$

Step 3. Put the values to find the term

Put the obtained value in the formula:

$$\begin{gathered} a_n=a_1+(n-1)d \\ {a}_{13}=16+(13-1)(-5) \\ {a}_{13}=16+\left(12\right)(-5) \\ {a}_{13}=16-60 \\ {a}_{13}=-44 \end{gathered}$$