Identify the 27th term of an arithmetic sequence where a₁ = 38 and a₁₇ = -74.

Solution:

The formula to find the nth term in an arithmetic sequence is

an = a₁ + (n - 1)d

Where a_n = nth term

a₁ = first term

n = term position

d = common difference

It is given that

a₁ = 38, a₁₇ = -74

a_n = a₁ + (n - 1)d

⇒ -74 = 38 + (17 - 1)d

⇒ -74 = 38 + 16d

⇒ 16d = -74 - 38

⇒ 16d = -112

⇒ d = -7

We know that

⇒ a₂₇ = a₁ + (n - 1) d

⇒ a₂₇ = 38 + (27 - 1)(-7)

⇒ a₂₇ = 38 + (26)(-7)

⇒ a₂₇ = 38 - 182

⇒ a₂₇ = -144

Therefore, the 27th term is -144.

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Identify the 27th term of an arithmetic sequence where a₁ = 38 and a₁₇ = -74.

Summary:

The 27th term of an arithmetic sequence where a₁ = 38 and a₁₇ = -74 is -144.