Q41. - Algebra 1

Question

Write an equation for the term of each arithmetic sequence.

$a_1=6, d=5$ 

Step-by-Step Solution

Answer

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

Step 1. Write the equation for the n th 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 n th term of the given arithmetic sequence having a 1 = 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 $5n+1$.