Question

How to find the next three terms in $2,5,10,17,26,...?$

Answer 1

Step 1. Identify the pattern of common difference

The first term is $2$

The second term is $5$

$\therefore 2+3=5$

Third term is $10$

$\therefore 5+5=10$

The fourth term is $17$

$\therefore 10+7=17$

The fifth term is $26$

$\therefore 17+9=26$

As a result, we are adding consecutive odd numbers starting from $3$ to each preceding terms.

Step 2. Find the next three terms

The next three terms is

$$\begin{gathered} 26+11=37 \\ 37+13=50 \\ 50+15=65 \end{gathered}$$

Hence the next three terms is $37,50$ and $65$