Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281.

Solution:

The n-th term of an arithmetic sequence is given by a_n = a + (n - 1)d

Given, a₁₈ = 97

a + (18 - 1) d = 97

a + 17d = 97 -------------- (1)

Also, a₂₀ = 281

a + (20 - 1) d = 281

a + 19 d = 281 ------------ (2)

Solving (1) and (2)

(2) - (1) we get, 19d - 17d = 184

2d = 184

d = 92

Now finding ist term a,

a + 17(92) = 97

a + 1564 = 97

a = -1467

To find n-th term,

 a_n = -1467 + (n - 1)92

 a_n = -1467 + 92n - 92

 a_n = 92n - 1559

Therefore, the value of a_n = 92n - 1559.

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Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281.

Summary:

The n-th term of the arithmetic sequence where a₁₈ = 97 and a₂₀ = 281 is 92n - 1559.