Question

Describe a pattern shown in this sequence, and use the pattern to find the next two terms.

7, 15, 23, 31, 39, _, _...?

*This is for geometry but we're reviewing old algebra stuff that I forgot thanks!*

Answer 1

This is an arithmetic sequence because each terms is a constant difference, called the common difference, from the term preceding it. Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number.

d=39-31=31-23=23-15, etc=8, and we can see a=7 so

a(n)=7+8(n-1) which we can simplify

a(n)=8n-1, so the 6th and 7th terms are:

47 and 55

Answer 2

The pattern is adding 8 to the previous number.
ex. 7+8=15, 15+8=23, 23+8=31, 31+8=39
Now for the next 2 terms:
39+8=47
47+8=55
Hope this helps!