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 = a₁ + (n - 1) d

Where d is the common difference

a_n is the nth term

a₁ is the first term

We know that

d = (a₁₅ - a₁₄)

d = (9 + 33)

d = 42

Substituting it in the formula

a₁₄ = a₁ + (n - 1) d

-33 = a₁ + (14 - 1) 42

-33 = a₁ + 546

a₁ = - 33 - 546

a₁ = -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.

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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.