Question

Find a formula for the nth term in this

Answer 1

Answer:

$a_n=6n-13$

Step-by-step 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:

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