Question

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

Answer 1

`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`

`nth` term `a_n = a_1 + (n-1) * d`

`:. a_19 = a_1 + (19-1) * d = -14 + 18 * 7 = -14 + 91 = 112`