Please check the given sequence is a combination of two series.
Series 1: 19, 38, 114, …
Series 2: 2,3,4

In series 1, Pattern followed is *2, *3, so next will be *4
Next term will be 114*4 = 456

===> 19*2 = 38

===>38*3 = 114

===>114*4 = 456

The number are 1² – 1 = 0,

2² – 2 = 2,

3² – 1 = 8,  

4² – 2 = 14,

5² – 1 = 24,…….

.’. Missing number = 5² – 1 = 24.

The numbers are 11², 15², 19²,… i.e. 11², (11 + 4 * 1)², (11 + 4 * 2)²,….
.’. Missing number =(11 + 4 * 3)² =  (23)² = 529.

The pattern is + 3, + 4,….
.’. Missing number = 9 + 5 = 14.

The pattern is + 5, + 7, + 9, + 11,…
.’. Missing number = 33 + 13 = 46.

8 * 0.5 = 4
4 * 1 = 4
4 * 2 = 8
8 * 4 = 32
32 * 8 = 256

8 + 1² + 1= 10
10 + 3² + 1= 20
20 + 5² + 1= 46……..

8 * 0.5 = 4
4 * 1 = 4
4 * 1.5 = 6
6 * 2 = 12
12 * 2.5 = 30

18 * 1 + 2 = 20
20 * 2 – 4 = 36
36 * 3 + 6 = 114
114 * 4 – 8 = 448
448 * 5 + 10 = 2250

11 + 1² + 1= 13
13 + 2² + 1= 18
18 + 4² + 1= 35……..

1650/6 – 5 = 275 – 5 = 270
270/5 -4 = 54-4 = 50
50/4 -3 = 12.5 -3 = 9.5
9.5/3 -2 = 3.17-2 = 1.17
1.17/2 -1 = 0.585-1 = -0.415

520*1/5 =104
104*2/5= 41.6
41.6*3/5 = 24.96
24.96*4/5 = 19.97

11*1+(1*7) =11+7 = 18
18*2+(2*6) = 36+12 = 48
48*3+(3*5) = 144+15 = 159
159*4+(4*4) = 636+16 = 652

Clearly, the given series consists of prime numbers starting from 2. The prime number after 11 is 13.
So, 13 is the missing number.

We can observe that the above series is square of odd numbers starting from one. So our answer will be 9^2 = 81.

Explanation:

5 + 7^2 = 5 + 49 = 54,
54 + 6^2 = 54 + 36 = 90,
90 + 5^2 = 90 + 25 = 115,
115 + 4^2 = 115 + 16 = 131,
131 + 3^2 = 131 + 9 = 140,
140 + 2^2 = 140 + 4 = 144.

So, the next number is 144.

The pattern is + 0.05, 0.10, + 0.15,….
.’. Missing number = 0.8 + 0.20 = 1.

8,29,113,449

2×4=8

8×4=32–3=29

29×4=116–3=113

113×4=452–3=449

449×4=1796–3=1793

Ans=1796

The odd terms form the sequence 1,3,5,7,……

Hence the next odd term is 9

even terms form the sequence 2,14,34,……

14=2+3*4

34=14+5*4

i.e an even term other than first even term 2 is obtained by

preceding even term +(preceding odd term*4)

so the next even term =34+(7*4)=34+28=62.

Hence the next two terms of the given sequence are 62,9 respectively.

pattern is * 2, * 3,*4, number is = 72 x 5 = 360.

Numbers are (2³ – 1), (3³ – 1), (4³ – 1), (5³ – 1), (6³ – 1), (7³ – 1) etc.

So, the next number is (8³ – 1) = (512 – 1) = 511.

This is a simple addition series. Each number increases by 2.

This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on

This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on.

Alternately, the numbers are increased by four and doubled to get the next number>
Thus, 10 + 4 = 14;
14 * 2 = 28;
28 + 4 = 32;
32 * 2 =64  and so on.
So, 132 is wrong and must be replaced by (68 * 2)  i.e.  136.

The pattern is + 5, + 7, + 9, + 11,…
.’. Missing number = 33 + 13 = 46.

(2*1) + 2 =4

(4*2) + 3 = 11

(11*3) + 4 =37

(37*4) + 5 = 153

Given series :

24 , 6 , 18 , 9 , 36 , 9 , 24 ,…

We are required to find the next term.

Let’s group the numbers into pairs

( 24 , 6 ) , ( 18 , 9 ) , ( 36 , 9 ) , ( 24 , _)

We see that,
24 ÷ 4 = 6
18 ÷ 2 = 9
36 ÷ 4 = 9

So, In first pair , first number divided by 4 to get second number.

In second pair, first number divided by 2 to get second number .

We can generalise that, For Even pair of the sequence from the beginning, we need to divide the first number in the pair by 2 to get second number.

For Odd pair of the sequence from the beginning, we need to divide the first number in the pair by 4 to get second number.

( 24 , _ ) is the fourth pair. We know that, For even pair , first number to be divided by 2

24 ÷ 2 = 12 ( Required number )