# Find an equation for the nth term of the arithmetic sequence. a14 = -33, a15 = 9.

**Solution:**

In an arithmetic sequence the formula to find the nth term is

a_{n} = a_{1} + (n - 1) d

Where d is the common difference

a_{n} is the nth term

a_{1} is the first term

We know that

d = (a_{15} - a_{14})

d = (9 + 33)

d = 42

Substituting it in the formula

a_{14} = a_{1} + (n - 1) d

-33 = a_{1 }+ (14 - 1) 42

-33 = a_{1 }+ 546

a_{1} = - 33 - 546

a_{1} = -579

The nth term of the arithmetic sequence is

a_{n} = -579 + (n - 1) 42

Therefore, an equation for the nth term is a_{n} = -579 + (n - 1) 42.

## Find an equation for the nth term of the arithmetic sequence. a14 = -33, a15 = 9.

**Summary:**

The equation for the nth term of the arithmetic sequence is an = -579 + (n - 1) 42.

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