What is the 32nd term of the arithmetic sequence where a₁ = -31 and a₉ = -119?

Solution:

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

Given the first term a = a₁ = -31

common difference = d = unknown

To find the common difference substitute in the formula, we get

a₉ = -119

⇒ a + (9 - 1)d = -119

⇒ a + 8d = -119

We know a = -31

⇒ -31 + 8d = -119

⇒ 8d = -119 + 31

⇒ 8d = -88

⇒ d = -11

Now, find a₃₂

a₃₂ = a + (32 - 1)d

a₃₂ = -31 + (32 - 1) × (-11)

a₃₂ = -31 + 31 × (-11)

a₃₂ = -31 + ( -341)

a₃₂ = -372

Therefore, the value of a₃₂ = -372.

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What is the 32nd term of the arithmetic sequence where a₁ = -31 and a₉ = -119?

Summary:

The 32^nd term of the arithmetic sequence where a₁ = -31 and a₉ = -119 is a₃₂ = -372.