What is the 22^nd term of the arithmetic sequence where a₁ = 8 and a₉ = 56?

Solution:

The nth 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 = 8 and a₉ = 56

We know that

a₉ = a₁ + (9 - 1)d

8 + 8d = 56

8d = 56 - 8

8d = 48

d = 6

Now we have to find the 22^nd term

a₂₂ = a₁ + (22 - 1)d

Substituting the values

a₂₂ = 8 + (21)(6)

a₂₂ = 8 + 126

So we get,

a₂₂ = 134

Therefore, the 22^nd term is 134.

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What is the 22^nd term of the arithmetic sequence where a₁ = 8 and a₉ = 56?

Summary:

The 22^nd term of the arithmetic sequence where a₁ = 8 and a₉ = 56 is 134.