Question

How do I find how many circles would be in the 5th term

Answer 1

You can notice that in the first term there is one circle, in the second term there are three cricles and in the third term are six circles.

Each of the previous term can be expressed as follow:

first term:

`2^0+0=1`

second term:

`2^1+1=3`

third term:

`2^2+2=6`

In gereral, you can write for the (n + 1)th term:

`2^n+n`

Thus, each term of the series can be expressed as the previoues expression indicates. The fourth term is the result for n=3 and the fifth term is the result for n=4. You replace and you obtain:

fifth term:

`2^4+4=16+4=20`

Hence, the fifth term will have 20 circles.