How do you write a rule for the nth term 7,5,3,1,-1?

2 Answers
Jun 27, 2018

each term is going down by 2

2n

this gives -2, -4, -6, -8

to get the sequence we need to find the adjuster

opposite of -2 is +2, 7+2=9

2n+9 or 92n

Jun 27, 2018

an=72n

Explanation:

First of all, notice that this is an arithmetic sequence, i.e. two consecutive terms differ by a common difference. In this case, two consecutive terms always differ by 2, which means that if you know the nth terms, you will get the n+1th by subtracting two.

We start from a0=7, which is the starting point of the sequence. The next term, a1, will be a02=72=5, and so on.

The general rule is what we just described with words: start from the initial value 7, and subtract 2 with each iteration. This means that, after k iterations, we will have subtracted two k times, i.e. we will have subtracted a total of 2k.

So, the rule is

an=72n

You can confirm this by building some terms using the definition: given the starting value a0, we have

a1=a012
a2=a12=(a02)2=a022
a3=a22=(a022)2=a032
a4=a32=(a032)2=a042

as you can see, the index of the term is equal to the times we have to subtract 2.