# The first three terms of an arithmetic series are x-1, 5x-3, 4x+5, how do you find the sixth term?

The sixth term is $31$

#### Explanation:

It should be

$5 x - 3 - \left(x - 1\right) = 4 x + 5 - \left(5 x - 3\right) \implies 4 x - 2 = 8 - x \implies 5 x = 10 \implies x = 2$

Hence the first three terms are $2 - 1 = 1$,$5 \cdot 2 - 3 = 7$,$4 \cdot 2 + 5 = 13$

So it is an arithmetic series with first term ${a}_{1} = 1$ and ratio $r = 6$

hence

${a}_{6} = {a}_{1} + \left(6 - 1\right) \cdot 6 = 1 + 30 = 31$