Question

Look for a pattern and find the next two numbers in the sequence and then write a general version of the nth term.

1 2 3 4 5 6 7 8 n
18 30 42 54 66 78

I can recognize the pattern as being + 12 so under 7 my answer would be 90 and under 8 my answer would be 102, but how do I figure out what the nth term would be?

Answer 1

As n increases by 1, the terms increases by 12. That means that if you add n to the term number, you add 12n to the value. So, start with

Tn = 12n

But T1=18, not 12. So, you need to add 6:

Tn = 12n+6

Or, you can use the general formula for an arithmetic progression with first term=a and common difference=d:

Tn = a + (n-1)d

You know that d=12 and a=18, so

Tn = 18 + (n-1)*12
= 18 + 12n - 12
= 6+12n