# How do you find the next four terms of the arithmetic sequence 31, 24, 17, ...?

Jan 7, 2017

The reqd. next four terms are,

${T}_{4} = 10 , \mathmr{and} , {T}_{5} = 3 , {T}_{6} = - 4 , {T}_{7} = - 11$.

#### Explanation:

We find that, for the given Arithmetic Sequence (A.S.),

The First Term $= a = 31 ,$ &, the Common Difference

$d = 24 - 31 = 17 - 24 = \ldots = - 7$.

Now, we know that, for such an A.S., ${T}_{n} = a + d \left(n - 1\right)$

$\therefore {T}_{n} = 31 - 7 \left(n - 1\right) = 38 - 7 n$.

Hence, the reqd. next four terms are,

${T}_{4} = 38 - 7 \left(4\right) = 10 , \text{ &, similarly, } {T}_{5} = 3 , {T}_{6} = - 4 , {T}_{7} = - 11$.