Explanation

Given series: 459, 440, ?, 402, 383

Difference between terms:  

459 - 440 = 19  

402 - 383 = 19  

Assuming constant difference of 19:  

? = 440 - 19 = 421

Explanation

Given sequence:  

10, 34, 50, 68, 88, ?

Now look at the differences between the numbers:

- 34 − 10 = 24  

- 50 − 34 = 16  

- 68 − 50 = 18  

- 88 − 68 = 20

The differences are: 24, 16, 18, 20

Now see the pattern in differences:

24, 16, 18, 20 → decreasing, then increasing by 2

So if this trend continues, the next difference should be:

22

88 + 22 = 110

Explanation

Explanation

o find the fourth proportional to 5, 10, 25, we use the formula:

(First : Second = Third : Fourth)  

So,  

5 : 10 = 25 : x  

⇒ (5/10) = (25/x)

Now cross-multiply:  

5x = 250  

x = 250 / 5  

x = 50

Explanation

Looks like pattern is:  

n → n × (n − 1)  

3 × 2 = 6  

4 × 3 = 12  

5 × 4 = 20  

6 × 5 = 30  

7 × 6 = 42

Explanation

6 → +7 → 13  

13 → +8 → 21  

21 → +9 → 30  

30 → +16 → 46  

Answer: 30  

Explanation

Each term is half of the previous term:  

2 → 1 (2 ÷ 2)  

1 → 1/2 (1 ÷ 2)  

1/2 → 1/4 (1/2 ÷ 2)  

So next term = 1/4 ÷ 2 = 1/8  

Explanation

 298 → 294 (−4)  

- 294 → 285 (−9)  

- 285 → 269 (−16)  

Now, see the pattern in the differences:

-4 (2²), -9 (3²), -16 (4²)

Next should be: −25 (5²)

So, 269 − 25 = 244

Explanation

Given series:  

63, 71, ?, 93, 107

Now find the differences between known consecutive numbers:

- 71 − 63 = 8

- ? − 71 = ?

- 93 − ? = ?

- 107 − 93 = 14

Let's check a consistent pattern in differences:

- 63 → 71 (+8)  

- 71 → ? (+10)  

- ? → 93 (+12)  

- 93 → 107 (+14)

So the pattern of differences is increasing by +2 each time:  

+8, +10, +12, +14

Now, insert the missing number:

- 71 + 10 = 81  

Explanation

10, 44, 12, 40, 14, 38

- 1st number series: 10 → 12 → 14 → ? (increasing by 2)

- 2nd number series: 44 → 40 → 38 → ? (decreasing by 4, then 2)

So:

- Next in first series: 14 + 2 = 16

- Next in second series: 38 - 4 = 34