Select the correct option will complete the given number series.

 

13, 10, 7, 4, ___

Given series follows the rule of

1050/2.5 = 420
420/2.5 = 168
168/2.5 = 67.2
so 67.2/2.5 = 26.88

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.

The series follow the rule,

21 = 
77 = 92-4
165 = 132-4
285 = 172-4

5,9,13,17,21,(+4)...
In the same way next no. will be
212-4 = 441 - 4 = 437

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 .

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.

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.

In this series, the third letter is repeated as the first letter of the next segment. The middle letter, A, remains static. The third letters are in alphabetical order, beginning with R.

Because the letters are the same, concentrate on the number series, which is a simple 2, 3, 4, 5, 6 series, and follows each letter in order.