Explanation:
Two series are mixed to form the given series.
$\boxed5$, 7, $\boxed{9}$, 11, $\boxed{14}$, 16, $\boxed{20}$, 22, $\boxed{27}$, 29, $\boxed{?}$.
I. 5, 9, 14, 20, 27 at a successive difference of 4, 5, 6, 7 ... and so on.
II. 7, 11, 16, 22, 29 at a successive difference of 4, 5, 6, 7 and so on.
Hence, the next term would be 27 + 8 = 35.
Explanation:
Numbers at the even positions are the squares of numbers at the odd positions. So next number is 36.
$\begin{array}{cc}
Number & Next\;number \\
1 & 1^2 \\[2px]
2 & 2^2 \\[2px]
3 & 3^2 \\[2px]
4 & 4^2 \\[2px]
5 & 5^2 \\[2px]
6 & \color{blue}{6^2 = 36} & \checkmark \\[2px]
\end{array}$
Explanation:
Three series are mixed to form the given series.
$\boxed{12}$, 11, 10, $\boxed{13}$, 18, 17, $\boxed{14}$, 25, 24, $\boxed{15}$, 32, 31, $\boxed{?}$
I. 12, 13, 14, 15, ... form one series
II. 11, 18, 25, 32, 39, ... form another series
III. 10, 17, 24, 31, 38 ... form another series.
So next number will be from the first series. $\therefore$ 16.
