Question

Write a formula for the nTh term of the sequence:1,4,7,10,13

Answer 1

`a_n=3n-2`

Step-by-step explanation:

The formula for the nth term of an arithmetic sequence is

`a_n=a_1+d(n-1)`

Where:

a_n is the term we want to find

a_1 is the first term of the sequence

d is the common distance between the terms.

In this sequence, we can see that d = 3. Because any term minus the previous is 3:

`\begin{gathered} 4-1=3 \\ 7-4=3 \\ 10-7=3 \\ 13-10=3 \end{gathered}`

The first term is 1. Then:

`a_n=1+3(n-1)`

Now, we can apply distributive property:

`a_n=1+3n-3=3n-2`

And we get the final expression for the arithmetic sequence formula for the nth term:

`a_=3n-2`