# How do you write the nth term rule for the sequence 4,1,-2,-5,-8,...?

Aug 22, 2016

${n}^{t h}$ term in given sequence is $7 - 3 n$.

#### Explanation:

This is an arithmetic sequence as the difference $d$ between a term and its preceding term is always $- 3$ as $- 3 = 1 - 4 = - 2 - 1 = - 5 - \left(- 2\right) = - 8 - \left(- 5\right)$.

If first term is ${a}_{1}$ and common difference in such arithmetic sequence is $d$,

${n}^{t h}$ term is given by a_1+(n-1)×d. Hence ${n}^{t h}$ term in given series is

4+(n-1)×(-3)

= $4 - 3 n + 3$

= $7 - 3 n$