Question

The first term of an AP is -7 and the ratio of the eight term to the third term is 7:1 calculate the common difference

Answer 1

the common difference is 6.

Explanation:

Given;

first term of an AP, a = -7

let the common difference = d

The third term is written as;

T₃ = a + 2d

The eight term is written as;

T₈ = a + 7d

The ratio of the eight term to third term = 7:1

`(T_8)/(T_3) = (7)/(1) = (a+ 7d)/(a + 2d) \\\\7 = (a+ 7d)/(a + 2d)\\\\Recall, a = -7\\\\7 = (-7+ 7d)/(-7 + 2d)\\\\7(-7 + 2d) = -7+ 7d\\\\-49 + 14d = -7 + 7d\\\\14d -7d = -7 + 49\\\\7d = 42\\\\d = (42)/(7) \\\\d = 6`

Therefore, the common difference is 6.