Explain how to write a formula for an arithmetic sequence.

you can use a linear form ax+b

Tn = a + (n-1) d

Step-by-step explanation:

In an arithmetic sequence, the value of the terms change in an arithmetic progression and not geometric progression. The value of the sequence of numbers is such that the difference between two consecutive terms is a common difference denoted by d.

Assuming the first term is a1, That means

The second term, a2 is a1 + d

The third term, a3 is a1 + 2d

The fourth term is a1 + 3d

Looking at the pattern above, as we progress, the number multiplying d is is always one lesser than the current term we are looking for. This means that for nth term, the number multiplying d would be n-1. Therefore,

The nth term, Tn will be

Tn = a + (n-1) d