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

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Answer 1 · 2016-08-22T21:33:41

$n^(th)$ term in given sequence is $7-3n$ .

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

If first term is $a_1$ and common difference in such arithmetic sequence is $d$ ,

$n^(th)$ term is given by $a_1+(n-1)×d$ . Hence $n^(th)$ term in given series is

$4+(n-1)×(-3)$

= $4-3n+3$

= $7-3n$

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