Find an equation for the nth term of the arithmetic sequence.
a₁₉ = -92, a₂₀ = 6

Solution:

It is given that in an arithmetic sequence,

a₁₉ = -92, a₂₀ = 6

So, Common difference = d

d = a₂₀ - a₁₉

d = 6 - (-92)

d = 6 + 92

d = 98

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

Substitute the value of n = 20

a₂₀ = a₁ + (20 - 1)d

6 = a₁ + 19(98)

6 = a₁ + 1862

6 - 1862 = a₁

-1856 = a₁

a₁ = -1856

Now nth term:

a_n = a₁ + (n - 1)d

a_n = -1856 + (n - 1)98

a_n = -1856 + 98(n - 1)

Therefore, a_n = -1856 + 98(n - 1) is an equation for the n^th term of the arithmetic sequence.

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Find an equation for the nth term of the arithmetic sequence.
a₁₉ = -92, a₂₀ = 6

Summary:

a_n = -1856 + 98(n - 1) is an equation for the nth term of the arithmetic sequence. a₁₉ = -92, a₂₀ = 6.