Question

Consider Akelia’s sequence 5, 8, 11, 14, 17, ….

a. If you believed in patterns, what might you say is the next number in the sequence?

Answer 1

It would be 20

Explanation:

As we can see, the sequence starts from 5 and increases by three each time. In fact, one possible formula for that sequence could be:

`a_n=3n+2\hspace{10}n\in N`

Let's confirm the formula by evaluating the first 6 terms:

`a_1=3(1)+2=3+2=5\\a_2=3(2)+2=6+2=8\\a_3=3(3)+2=9+2=11\\a_4=3(4)+2=12+2=14\\a_5=3(5)+2=15+2=17\\a_6=3(6)+2=18+2=20`