Q6. - Algebra 1

Question

Write an equation for the nth term of the arithmetic sequence shown below.

 

            -2,1,4,7,10,13,…..

 

F $a_n=2n-1$

G $a_n=2n+4$

H $a_n=3n+2$

J $a_n=3n-5$

Step-by-Step Solution

Answer

The nth term of the arithmetic sequence is given as $a_n=3n-5$.

Option J is correct.

Step 1. State the concept of arithmetic sequence.

In an Arithmetic Sequence the difference between one term and the next is a constant.

The nth term of the Arithmetic sequence is given by the formula

$$\begin{gathered} a_n=a+\left(n-1\right)d \\ d=a_2-a_1 \end{gathered}$$

Where, $a_1=a=$ first term and $d=$ common difference.

Step 2. Find the common difference.

The common difference is given as:

$$\begin{gathered} d=a_2-a_1 \\ d=1-\left(-2\right) \\ d=1+2 \\ d=3 \end{gathered}$$

Step 3. Find the nth term of the arithmetic sequence.

The nth term of the arithmetic sequence is calculated as follows.

 $$\begin{gathered} a_n=a+\left(n-1\right)d \\ =-2+\left(n-1\right)3 \\ =-2+3n-3 \\ {a}_n=3n-5 \end{gathered}$$ 

Therefore, option J is correct.