Number Series Questions

Here the first letter of the group is moved with a gap of one letter, the second letter of the group is backwardness and the third letter of the group is forwardness proceeding like this we get the letter group "JGW"

$$\begin{gathered} 2 = 12 + 1 \\ 3 = 22 - 1 \\ 10 = 32 + 1 \\ Now 102 - 1 = 99 \\ 9802 = 992 + 1 \end{gathered}$$

The given number series is  21 56 102 160 231 316

21      56       102        160      231       316         416

   +35    +46       +58       +71      +85       +100

        +11      +12       +13      +14      +15

Hence, the next number in the given number series is 316 + 100 = 416.

The pattern is x1+3, x 2, x1+3, x 3, x1+3, x 4

The next number=60x4=240

Given number 8, 6, 9, 23, ?

The pattern of given series is:

8 x 1 - 2 = 6 6 x 2 - 3 = 9 9 x3 - 4 = 23 23 x4 - 5 = 87