# What is the 32nd term of the arithmetic sequence where a_{1} = 14 and a_{13} = -58?

**Solution:**

Given: First term a = a_{1} = 14

The common difference is not known.

To find:32^{nd} term = a_{32}

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

To find the common difference 'd' substitute in the formula, we get

a_{13} = -58

⇒ a + (13 - 1) d = -58

⇒ 14 + 12d = -58

⇒ 12d = -58 -14

⇒ 12d = -72

⇒ d = -6

Now find a_{32}

a_{32} = a + (32 -1 ) × d

a_{32} = 14 + 31 × (-6)

a_{32} = 14 + (-186)

a_{32} = -172

Therefore, the value of a_{32 }= -172.

## What is the 32nd term of the arithmetic sequence where a1 = 14 and a13 = -58?

**Summary:**

The 32nd term of the arithmetic sequence where a_{1} = 14 and a_{13} = -58 is a_{32} = -172.