# Find an equation for the nth term of the arithmetic sequence.

a_{16} = 21, a_{17} = -1

**Solution:**

It is given that,

a_{16} = 21, a_{17} = -1

So, common difference = d

d = a_{17} - a_{16}

d = -1 - 21

d = -22

We know that the formula for nth term a_{n} = a_{1} + (n - 1)d

Substitute the value of n = 16, we get

a_{16} = a_{1} + (16 - 1)d

21 = a_{1} + 15(-22)

21 = a_{1} - 330

21 + 330 = a_{1}

a_{1} = 351

Now nth term:

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

a_{n} = 351 + (n - 1)(-22)

a_{n} = 351 - 22(n - 1)

a_{n} = 351 + 22 - 22n

a_{n} = 373 - 22n

Therefore, a_{n} = 373 - 22n is an equation for the nth term of the arithmetic sequence.

## Find an equation for the nth term of the arithmetic sequence.

a16 = 21, a17 = -1

**Summary:**

a_{n} = 373 - 22n is an equation for the nth term of the arithmetic sequence. a16 = 21, a17 = -1.