Question

Find a formula for the nth term in this

arithmetic sequence:
a1 = -7, 22 = -1, a3 = 5, 24 = 11, ...

Answer 1

`a_n=6n-13`

Explanation:

Arithmetic Sequences

The arithmetic sequences can be identified because each term is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

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

Here a1 is the first term and r is the common difference.

The given sequence is:

`a_1=-7, a_2=-1,a_3=5,a_4=11,...`

We can find the common difference by subtracting successive terms:

`a_2-a_1=-1+7=6`

`a_3-a_2=5+1=6`

`a_4-a_3=11-5=6`

Since all the differences are equal, r=6. Thus, the general term is:

`a_n=-7+6(n-1)`

Operating:

`a_n=-7+6n-6`

`a_n=6n-13`

The nth term is:

`\mathbf{a_n=6n-13}`