# How do you find the 19th term in the sequence -14, -7, 0, 7, 14,.. ?

Mar 17, 2018

color(green)(a_19 = 112

#### Explanation:

${a}_{1} = - 14 , {a}_{2} = - 7 , {a}_{3} = 0 , {a}_{4} = 7 , {a}_{5} = 14$

${a}_{2} - {a}_{1} = {a}_{3} - {a}_{2} = {a}_{4} - {a}_{3} = {a}_{5} - {a}_{4} = d = 7$

Now we know, ${a}_{1} = - 14 , d = 7$

$n t h$ term ${a}_{n} = {a}_{1} + \left(n - 1\right) \cdot d$

$\therefore {a}_{19} = {a}_{1} + \left(19 - 1\right) \cdot d = - 14 + 18 \cdot 7 = - 14 + 91 = 112$