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# Identify the 27th term of an arithmetic sequence where a_{1} = 38 and a_{17} = -74.

**Solution:**

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

an = a_{1} + (n - 1)d

Where a_{n} = nth term

a_{1} = first term

n = term position

It is given that

a_{1} = 38, a_{17} = -74

a_{n} = a_{1 }+ (n - 1)d

⇒ -74 = 38 + (17 - 1)d

⇒ -74 = 38 + 16d

⇒ 16d = -74 - 38

⇒ 16d = -112

⇒ d = -7

We know that

⇒ a_{27} = a_{1} + (n - 1) d

⇒ a_{27} = 38 + (27 - 1)(-7)

⇒ a_{27} = 38 + (26)(-7)

⇒ a_{27} = 38 - 182

⇒ a_{27} = -144

Therefore, the 27th term is -144.

## Identify the 27th term of an arithmetic sequence where a_{1} = 38 and a_{17} = -74.

**Summary:**

The 27th term of an arithmetic sequence where a_{1} = 38 and a_{17} = -74 is -144.

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