Number Series Questions

The given number series 9, 19, 21, 43, 45, ... follows a pattern that

ALternately (x 2 + 1) and  (x 1 + 2)

9 

9 x 2 + 1 = 19

19 x 1 + 2 = 21

21 x 2 + 1 = 43

43 x 1 + 2 = 45

45 x 2 + 1 = 91

Hence, the next number in the given sequence is 91.

The letters move 2, 2, 3, 3, 4, 4, ... steps forward.

By trial and error method from the given options,

'1' satisfies the above given equation.

The first letter moves three steps forward. The second letter moves two steps forward. The third letter moves three steps forward.

The given sequence is a combination of three series:
i)1st, 4th, 7th terms i.e, 2, 4, 9
ii)2nd, 5th, 8th terms i.e, 3, 6, 12
iii)3rd, 6th, 9th terms i.e, 4, 8, 16
In each one of i, ii, iii, each term is twice the preceding term.
So, 9 is wrong and must be replaced by (4*2) = 8

This is an alternating series in alphabetical order. The middle letters follow the order ABCDE. The first and third letters are alphabetical beginning with J. The third letter is repeated as a first letter in each subsequent three-letter segment.

The given number series 999, 990, 998, 991, 997, 992, ?

It follows a pattern that,

999

999 - 9 = 990

990 + 8 = 998

998 - 7 = 991

991 + 6 = 997

997 - 5 = 992

992 + 4 = 996

Hence, the next number in the given number series is 996.