1st term = 120
2nd term = 120-21 = 99
3rd term = 99-19 = 80
4th term = 80 - 17 = 63
5th term = 63 - 15 = 48

⇒ For every next term , preious term is substracteed in the order: -21, -19, -17, -15, -13,.....

So, missing term = 48 - 13 = 35

The digits are removed one by one from the beginning and the end in order alternately.

So, as to obtain the subsequent terms of the series.
1st term = 589654237
2nd term = 89654237
3rd term = 8965423
4th term = 965423
5th term = 96542

Each term in the series is obtained by adding 1 to the square of the preceding term.

So, missing term = (101)² + 1 = 10202.

1st term = 2 x 3 = 6
2nd term = 6 x 3 = 18
3rd term = 18 x 3 = 54,.....
⇒ Series is a G.P. in which a = 2, r = 3.

∴ 8th term = ar^8-1 = ar⁷ = 2 x 3⁷ = (2 x 2187) = 4374.

1st term = 125
2nd term = 125 - 45 = 80
3rd term = 80 - 35 = 45
4th term = 45- 25 = 20

⇒ For every next term, preious term is substracteed in the order: - 45, - 35, - 25, .....

So, missing term = 20 - 15 = 5

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.

1st term = 1
2nd term = 1 * 2 = 2
3rd term = 2 * 3/2 = 3
4th term = 3 * 2 = 6
5th term = 6 * 3/2 = 9
6th term = 9 * 2 =18
7th term = ?
8th term = 54

⇒ For every even position term, the previous term is multiplied by 2 and for the odd positioned term, the previous term is multiplied by 3/2

So, missing term = 18 x 3/2 = 27.

1st term = 6
2nd term = (6 * 2) + 1 = 13
3rd term = (13 * 2) -1 = 25
4th term = (25 * 2) +1 = 51
5th term = (51 * 2) - 1 = 101
6th term = ?

⇒ For every even position term, the previous term is multiplied by 2 and then  1 is added and for the odd positioned term, the previous term is multiplied by 2 and 1 is substracted

So, missing term = (101 * 2) + 1 = 203.

1st term = 5
2nd term = 5 + 1 = 6
3rd term = 6 + 3 = 6 + (1 + 2) = 9
4th term = 9 + 6 = 9 + (1 + 2 + 3) = 15
5th term = x
6th term = 40

⇒ For every term previous term is added with sumation of it previous position i.e. next term = previous term + ∑ (position -1)

So, missing term = 15 + (1 + 2 + 3 + 4) = 25

The sum of any three consecutive terms of the series gives the next term i.e.
► 1 + 3 + 4 = 8
► 3 + 4 + 8 = 15
► 4 + 8 + 15 = 27

∴ Missing number = 8 + 15 + 27 = 50

The given sequence is a combination of two series:

• 3, 7, 13, 21, 31, ?
  For every next term = previous term + 2 * its position
  i.e. 3, 3+2*2, 7 +3*2,  13 + 4*2 ....
• 4, 7, 13, 22, 34
  For every next term = previous term + 3 * (its position-1)
  i.e. 4, 4+3*1, 7 +3*2,  13 + 3*3 ....

So, missing term = 31 + 2*6 = 43.
As missing term lies in 1st pattern.

1st term = 198
2nd term = 198 - 4 = 198 - 2² = 194
3rd term = 194 - 9 = 198 - 3² = 185
4th term = 185 - 16 = 185 - 4² = 169

⇒ For next term, square of its positon is substracted from the previous term

So, missing pattern = 169 - 5² = 169 - 25 = 144.

Clearly, the given series consists of prime numbers starting from 2.

So, the missing term is the prime number after 11, which is 13.

1st term = 6
2nd term = 6 + 6 = 6 + 2*3 = 12
3rd term = 12 + 9 = 12 + 3*3 = 21
4th term = ?
5th term = 48  

⇒ For every next term, thrice its positon is added o the previous term.

So, missing term = 21 + 3*4 = 33.

1st term = 5 x 2 = 10
2nd term = 10 x 2 = 20
3rd term = 20 x 2 = 40,.....

⇒ Series is a G.P. in which a = 5 and r = 2.

Let 1280 be the n^th term of the series.
⇒ 5 x 2^n-1 = 1280
⇒ 2^n-1 = 256 = 2⁸
⇒ n - 1 = 8
⇒ n = 9

1st term = 2
2nd term = 2 + 3 = 2 + (2+1) = 5
3rd term = 5 + 4 = 5 + (3+1) = 9...

⇒ For next term, its position +1 is added to the previous term

So, missing term = 9 + 5 = 14

1st term = 2
2nd term = 2 + 1 = 3
3rd term = 3 * 1 = 3
4th term = 3 + 2 = 5
5th term = 5 * 2 = 10
6th term = 10 + 3 = 13...

⇒ For every term at even position, previous term is added with half of the position
⇒ For every term at odd position, previous term is multipiled with the same numeber that was added in previous term

So, missing term = 13 x 3 = 39.

⇒ For every term at even position, previous term is multiplied with the position+1
⇒ For every term at odd position, previous term is added with the position+1

So, missing term = 1127 + 8 = 1135.

The given sequence is a combination of three series:

• 1st, 4th, 7th, 10th, 13th terms i.e. 2, 4, 6, 8,?
• 2nd, 5th, 8th, 11th terms i.e. 1, 4, 7, 10
• 3rd, 6th, 9th, 12th terms i.e. 2, 5, 8, 11

Clearly, I consist of consecutive even numbers. So, the missing term is 10.

• The given series consists of cubes of natural numbers only.
• 256 is not the cube of any natural number.

The given sequence is a combination of two series:

• 13, 24, 35, 46, 57
• 32, 43, ?, 65, 76

In both series are in A.P. with common difference of 11.

So, missing term = 43 + 11 = 54.

1st term = 22
2nd term = 22 + 2 = 22 + 2¹ = 24
3rd term = 24 + 4 = 22 + 2² = 28
4th term =?
5th term = 52
6th term = 52 + 32 = 52 + 2⁵ =84

⇒ For next term, preivous term is add with 2 to the power of the position-1.
i.e. any term = previous term + 2^{(position - 1)}

So, missing term = 28 + 8 = 22 + 2³ = 36

1st term = (2² - 1)
2nd term = (4² - 1)
3rd term= ?
4th term = (8² - 1)
5th term = (10² - 1)
6th term = (12² - 1)

⇒ nth term = (n * 2)² - 1 

So, missing term = (6² - 1) = (36 - 1) = 35

Clearly the pattern is:

► 90 = 30 x 3,
► 180 = 6 x 30,
► 12 = 2 x 6,
► 50 = 25 x 2,
► 100 = 4 x 25,
► 200 = 50 x 4.

So, missing term = 3 x 50 = 150.

Alternatively,

The pattern is the combination of 2 series:

• 90, 180, 12, 50, 100, 200, ?
• 3, 50, 4, 25, 2, 6, 30, 3

after reversing 2nd series, i.e. 3, 30, 6, 2, 25, 4, 50, 3
on dividing term of the same position would give next term of reversed series.
i.e.

► 90/3 = 30
► 180/30 = 6
► 12/6 = 2
► 50/2 = 25
► 100/25 = 4
► 200/ 4 =50
► ?/50 = 3

So, missing term = 3 x 50 = 150.

1st term = 48
2nd term = 48/2 = 24
3rd term = 24 * 4 = 96
4th term = 96/2 = 48
5th term = 48 * 4 = 192...

⇒ For every term at even position, previous term is divided by 2
⇒ For every term at odd position, previous term is multipiled with 4

So, missing term = 192 ÷ 2 = 96.