# Identify the 42nd term of an arithmetic sequence where a_{1} = -12 and a_{27} = 66.

**Solution:**

Given, a_{1} = -12 and a_{27} = 66

We have to find the 42nd term of an arithmetic sequence.

The n-th term of an arithmetic sequence is given by a_{n} = a + (n - 1)d

So, a + (27 - 1) d = 66

-12 + 26 d = 66

26d = 66 + 12

26d = 78

d = 3

Now find a_{42}

a_{42} = a + (42 -1) × d

a_{42} = -12 + 41 × 3

a_{42} = -12 + 123

a_{42} = 111

Therefore, the value of a_{42} = 111.

## Identify the 42nd term of an arithmetic sequence where a_{1} = -12 and a_{27} = 66.

**Summary:**

The 42nd term of the arithmetic sequence where a_{1} = -12 and a_{27} = 66 is a_{42} = 111.

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