Identify the 31st term of an arithmetic sequence where a₁ = 26 and a₂₂ = -226.

Solution:

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

Given, a₁ = 26, a₂₂ = -226

a + (22 - 1) d = -226

a + 21d = -226

We know a = 26

26 + 21d = -226

21d = -226 - 26

21d = -252

d = -252/21

d = -12

Now, find a₃₂

a₃₁ = a + (31 - 1)d

a₃₁ = 26 + (31 - 1) × (-12)

a₃₁ = 26 + 30 × (-12)

a₃₁ = 26 - 360

a₃₁ = -334

Therefore the value of a₃₁ = -334.

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Identify the 31st term of an arithmetic sequence where a₁ = 26 and a₂₂ = -226.

Summary:

The 31st term of the arithmetic sequence where a₁ = 26 and a₂₂ = -226 is -334.