Number Series Questions

Z - 2 = X
X - 5 = S
S - 10 = I
I - 17 = R
R - 26 = R
R - 37 = G
G - 50 = I
The series 2, 5, 10, 17, 26, 37, 50 is obtained by the pattern +3, +5, +7, +9, . . . .

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 .

Let first no. be "k" and multiple be "l"...start value of y with 3
then,
[(k x y) + {l x (l-1)}]
Thus, we get

15 x 3 + 3 x 2 = 51
51 x 4 + 4 x 3 = 216
216 x 5 + 5 x 4 = 1100
1100 x 6 + 6 x 5 = 6630
6630 x 7 + 7 x 6 = 46452

Therefore, the missing number is 6630.

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"

Each term of the series is the product of the preceding two terms
So, 5000 is wrong and it must be replaced by (500*50) = 25000

The given series follows a pattern that,

19 x 19 x 19 = 6859

18 x 18 x 18 = 5832

17 x 17 x 17 = 4913

16 x 16 x 16 = 4096

15 x 15 x 15 = 3375

So, the missing number in the given series = 4913  

Here the letter series is alternative reverse order series. So we get P, N.

The given series follows the pattern that

So the missing number is  37 + 38 = 75

75 + 66 = 141

....