mat ns ans

 Explanation:

Take a Look at this series :

2³ – 2² = 8 – 4 = 4

3³ – 3² = 27 – 9 = 18

4³ – 4² = 64 – 16 = 48

5³ – 5² = 125 – 25 = 100

6³ – 6² = 216 – 36 = 180

7³ – 7² = 343 – 49 = 294

8³ – 8² = 512 – 64 = 448

Divide into two series

1st series 3,5,7,9

2nd series 5,19,41,? They are formed by taking numbers alternately

2nd Position: 2 + 3 *1 = 5

4th Position: 4 + 5*3 = 19

6th Position: 6 + 7*5 = 41

8th Position : 8 + 9*7 = 71

1st, 3rd, 5th…. position are odd numbers increasing order.

Answer is 71.

Here 2nd number = (1st number x 1 )+1

 3rd number = (2nd number x 2 +2) 

4th number = (3rd number x 3 )+3 and so on..

Therefore, 5th number = (4th number x 4) +4 =57 x 4 + 4 =232.

7 × 1 + 1 = 8

8 × 2 + 2 = 18

18 × 3 + 3 = 57

57 × 4 + 4 = 232

232 × 5 + 5 = 1165

Take a Look at the below sereies

2×1+(12)=32×1+12=3

3×2+(22)=103×2+22=10

10×3+(32)=3910×3+32=39

39×4+(42)=17239×4+42=172

<span class="highlight" style="box-sizing: border-box; font-size: 1.2em; font-weight: 600; white-space: normal;">Explanation:</span><br style="box-sizing: border-box; color: #222222; font-size: 13px; white-space: normal;">

The series follow the rule,

 

21 = 
77 = 92−492-4
165 = 132−4132-4
285 = 172−4172-4

5,9,13,17,21,(+4)...
In the same way next no. will be
212−4212-4 = 441 - 4 = 437

172×5+(52)=885

12 x 10 = 120

11 x 9 = 99

10 x 8 = 80

9 x 7 = 63

8 x 6 = 48

7 x 5 = 35

The pattern followed here is: 63 - 7 = 56; 56 - 6 = 50; 50 - 7 = 43; 43 - 6 = 37; 37 - 7 = 30; 30 - 6 = 24. Hence, the correct answer is ‘24’.

The given sequence consists of pairs of consecutive prime numbers.

The series consists of squares and cubes of consecutive natural numbers i.e. 12, 13, 22, 23, 32, 33, 42, .....

So, missing term = 43 = 64.

The given series follows a logic that

11 x 12, 12 x 13, 13 x 14, 14 x 15, 15 x 16,...

So the missing number is 13 x 14 = 182