Find an equation for the nth term of the arithmetic sequence.
a₁₆ = 21, a₁₇ = -1

Solution:

It is given that,

a₁₆ = 21, a₁₇ = -1

So, common difference = d

d = a₁₇ - a₁₆

d = -1 - 21

d = -22

We know that the formula for nth term a_n = a₁ + (n - 1)d

Substitute the value of n = 16, we get

a₁₆ = a₁ + (16 - 1)d

21 = a₁ + 15(-22)

21 = a₁ - 330

21 + 330 = a₁

a₁ = 351

Now nth term:

a_n = a₁ + (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.

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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.