Question

Insert the missing number $2,8,5,6,8,?,11$

Answer 1

Find the number:

In the sequence $2,8,5,6,8,?,11$,

Numbers at odd place are increasing by $3$

Numbers at even place are decreasing by $2$

$$\begin{gathered} a_n=\left\{\begin{array}{l}{a}_1+3\left(\frac{n-1}{2}\right)\mathrm{when}n\mathrm{is}\mathrm{odd}\\ a_2+\left(-2\right)\left(\frac{n}{2}-1\right)\mathrm{when}n\mathrm{is}\mathrm{even}\end{array}\right. \\ \therefore a_6=8-2\left(3-1\right) \\ =4 \end{gathered}$$

Hence, the missing number in the sequence is $4$