Question

Write an equation for the term of each arithmetic sequence.

$a_1=6,d=5$

Short answer

The equation for nth term of the given arithmetic sequence is $5n+1$.

Step-by-step solution

Step 1. Write the equation for the nth term of the arithmetic sequence.

The nth term of the arithmetic sequence $\left(a_n\right)$is given by:

$a_n=a_1+\left(n-1\right)d$

Where,$a_1$ is the first term of the arithmetic sequence and d is the common difference of the arithmetic sequence.

Step 2. Write an equation for the nth term of the given arithmetic sequence having a1=6 and d=5.

It is given that$a_1=6$ and $d=5$.

The equation for nth term of the given arithmetic sequence is given by:

$$\begin{gathered} a_n=a_1+\left(n-1\right)d \\ =6+\left(n-1\right)5 \\ =6+5n-5 \\ =5n+6-5 \\ =5n+1 \end{gathered}$$

Therefore, the equation for nth term of the given arithmetic sequence is $5n+1$.