Question

Study the following pattern and write the next three steps.

$$\begin{gathered} 2+4=2x3 \\ 2+4+6=3x4 \\ 2+4+6+8=4x5 \end{gathered}$$

Answer 1

Given pattern is

$$\begin{gathered} 2+4=2x3 \\ 2+4+6=3x4 \\ 2+4+6+8=4x5 \end{gathered}$$

Here, we see that sum of consecutive even integers starting from $2$ is equal to product of (number of even integers) to (number of even integers $+1$)

So, the pattern can be followed as,

$$\begin{gathered} 2+4=2x3 \\ 2+4+6=3x4 \\ 2+4+6+8=4x5 \\ 2+4+6+8+10=5\times 6 \\ 2+4+6+8+10+12=6\times 7 \\ 2+4+6+8+10+12+14=7\times 8 \end{gathered}$$

Hence, the next three steps are as mentioned above.