# How do you write a rule for the nth term of the arithmetic sequence given a_{20 }= 240, a_{15 }= 170?

**Solution:**

The nth term an of an arithmetic sequence with a_{1} as the first term and d as the common difference

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

a_{20} = a_{1} + 19d = 240 --- (1)

a_{15} = a_{1} + 14d = 170 --- (2)

Subtracting equation (2) from (1)

⇒ 5d = 70

Divide both sides by 5

⇒ d = 14

Substituting the value of d in equation 2

⇒ a_{1} + 14 (14) = 170

⇒ a_{1} + 196 = 170

⇒ a_{1} = 170 - 196

⇒ a_{1 }= -26

So we get,

⇒ a_{n} = -26 + (n - 1)(14)

⇒ a_{n} = -26 + 14n - 14

⇒ a_{n} = 14n - 40

Therefore, a rule for the nth term of the arithmetic sequence is a_{n} = 14n - 40.

## How do you write a rule for the nth term of the arithmetic sequence given a_{20} = 240, a_{15} = 170?

**Summary:**

The rule for the nth term of the arithmetic sequence given a_{20} = 240, a_{15} = 170 is a_{n} = 14n - 40.

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