Number Series Questions

Here the number follows the given rule 

 $$\begin{gathered} 23-1, 33-1, 43-1, 53-1, ... \\ \end{gathered}$$

But 28 has been given in problem series.

so 28 is wrong number.

Clearly, the numerators of the fractions in the given sequence follow the series of 2, 3, 5, 7,... and the denominator follows 3, 9, 27, 81, 243, ...
Then, the next term in the given sequence is  935 = 9243 = 127 .

The given number series is 10, 6, 8, 15, ?

10

10 x 0.5 + 1 = 6

6 x 1 + 2 = 8

8 x 1.5 + 3 = 15

15 x 2 + 4 = 34

Hence, the next number in the given series is 34.

Clearly, alternatively we add and subtract 10% of a term to obtain the next term of the series.
Thus, 10000 + (10% of 10000)= 11000;
11000 - (10% of 11000) = 9900;
 9900 + (10% of 9900)  = 10890;
10890 - (10% of 10890) = 9801.
 9801 + (10% of 9801)  = 9801+980 = 10781.
So, missing term = 10890- (10% of 10890)= 9801.

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

The given series is 1, 2, 6, 21, 88, ?

1

1 x 1 + 1 = 2

2 x 2 + 2 = 6

6 x 3 + 3 = 21

21 x 4 + 4 = 88

88 x 5 + 5 = 445

Hence, the next number in the given number sequence is 445.

First difference is 6 and second is 12. But if we take third as 18, then fourth difference will be 24. Then 93 can not be the last term.

So we have to take the difference as 6, 12, 24 and 48. 

So Answer is 21+24 = 45