# How do you write a rule for the nth term of the arithmetic sequence and then find a_22 given d=14, a_6=-10?

Sep 9, 2017

${a}_{n} = {a}_{1} + \left(n - 1\right) d , {a}_{22} = 214$

#### Explanation:

For arithmatic progression series ,

$n$ th term is ${a}_{n} = {a}_{1} + \left(n - 1\right) d$, where ${a}_{1.} n , d$ are

first term , number of terms and common difference respectively.

a_6=-10 , d=14 , n=6 , a_1= ? :. -10 = a_1+(6-1)*14

or  a_1= -10-70= -80 ; a_22=?

${a}_{22} = {a}_{1} + \left(n - 1\right) d \mathmr{and} {a}_{22} = - 80 + \left(22 - 1\right) \cdot 14$ or

${a}_{22} = - 80 + 294 = 214$ [Ans]