Question

What is the next number in the pattern below? 3, 5, 9, 15, 23, ___ 31 33 35 37

Answer 1

Each term in this pattern is created by adding consecutive multiples of 2 to the previous term.
$a_1=3 \\ a_2=3+ 2 \times 1=5 \\ a_3=5+2 \times 2=9 \\ a_4=9+2 \times 3=15 \\ a_5=15+2 \times 4=23$

You can write the formula for this pattern as:
$\left \{ {{a_1=3} \atop {a_n=a_{n-1}+2(n-1)}} \right.$

The next number is $23+2 \times 5=23+10=33$.
The answer is 33.