What is the 32^nd term of the arithmetic sequence where a₁ = 12 and a₁₃ = -60?

Solution:

The n^th term of an arithmetic sequence whose first term is a₁ and common difference is d is

⇒ a₁ + (n - 1)d

It is given that

a₁ = 12 and a₁₃ = -60

We know that

a₁₃ = a₁ + (13 - 1)d

12 + 12d = -60

12d = -60 - 12

12d = -72

d = -72/12

d = -6

Now we have to find the 32^nd term

a₃₂ = a₁ + (32 - 1)d

Substituting the values

a₃₂ = 12 + (31)(-6)

a₃₂ = 12 - 186

So we get,

a₃₂ = -174

Therefore, the 32^nd term is -174.

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What is the 32^nd term of the arithmetic sequence where a₁ = 12 and a₁₃ = -60?

Summary:

The 32^nd term of the arithmetic sequence where a₁ = 12 and a₁₃ = -60 is -174.