# How do you find the explicit formula for the arithmetic sequence, then find a_14 given a_1=9, d=-5?

##### 1 Answer
Mar 17, 2018

color(red)(a_14 = -56

#### Explanation:

${a}_{1} = 9 , d = - 5$

${a}_{2} = {a}_{1} + d = 9 - 5 = 4$

${a}_{3} = {a}_{2} + d = {a}_{1} + 2 d = {a}_{1} + \left(3 - 1\right) d = 4 - 5 = - 1$

$\therefore {a}_{n} = {a}_{1} + \left(n - 1\right) \cdot d$ is the explicit formula.

${a}_{14} = {a}_{1} + \left(14 - 1\right) \cdot - 5 = 9 - 65 = - 56$