Number Series Reasoning

Each of the numbers is doubled and 1, 2, 3, 4, 5, 6 is added in next term,
so, 89 × 2 + 6 = 184.

16 = 5 × 3 + 1, 51 = 16 × 3 + 3, 158 = 51 × 3 + 5
∴ Next term = 158 × 3 + 7 = 481

Second term is greater than first term by 5, while the third term is less than the second term by 3. The same order is repeated.

There are two alternate series
Series I: 6.25, 12.25, 20.25, 30.25 (sequence is +6, +8, +10)
Series II: 9, 16, 25, 36, (sequence is +7, +9, +11)

The given series consists of 2 series
(i) 2, 4, 6, 8 .............
(ii) 2, 4, 8 .............
Series (i) → 2× 1, 2 × 2, 2 × 3 , 2 × 4 .......
Series (ii) → 2, 2× 2, 4 × 2, 8 × 2 = 16 .......

1³ + 1² = 2, 2³ + 2² = 12, 3³ + 3² = 36 and so on
∴ 6³ + 6² = 252

The difference in consecutive numbers follows the sequence, 10, 40, 160.
So the next difference = 160 × 4 = 640
Therefore number = 213 + 640 = 853.

2+3 = 5, 5+2 = 7, 7+5 = 12, 12+3 = 15, 15+2 = 17, 17+5 = 22.
Note that 3,2,5 are being added that order to various numbers to get the next number. Therefore, 3 should be added to 22 to get the answer.

8 × 2 – 1 = 15,
15 × 2 – 2 = 28,
28 × 2 – 3 = 53,
53 × 2 – 4 =102

The numbers are 3 × 1², 3 × 2², 3 × 3², 3 × 4², 3 × 5², 3 × 6², ......
∴ Missing number = 3 × 7² = 3 × 49 = 147

The odd terms are squares of the numbers 1, 3, 5, .... while the even terms are cubes of the numbers 2,4,6,....

There are two alternate series.
1st series : 3, 4, 5, 6, 7 ........ and so on.
2nd series : 15, 16, 17,18, 19 ....... and so on.

Ratios of two consecutive terms are
1, ½, ⅓, ¼, and ⅕ respectively.

Clearly the given series is 1³ – 1, 2³ – 1, 3³ – 1, 4³ – 1, 5³ – 1, 6³ – 1.
So, the missing number is 4³ – 1 = 63.

The numbers in the series are square of 2,4,6 ...,10,12 .
Therefore, the missing number is square of 8 i.e., 8² = 64.

The common differences between the consecutive terms of the series are 6, 9, 12, 15, etc.

Differences between two consecutive terms are 2, 3, 4, 5 and 6 respectively.

The sequence followed in the series is ÷5, –5 which is repeated.

∴ 900 should be in place of 905.

There are 2 series :
3, 8, 13, 18, 23 and 2, 12, 22, 32, 42. Hence 9 is wrong.

If 27 is replaced by 36, then the ratios of two consecutive terms are 3/2, 2, 5/2, 3, ...

The series is
2³ – 1, 3³ – 1, 4³ – 1, 5³ – 1, 6³ – 1, 7³ – 1, 8³ – 1

The given sequence is a combination of two series:
I. 11, 21, 32, 41, 51 and II. 2, 3, 4, 5, 6
Clearly, the pattern in I is +10
So, 32 is wrong and should be replaced by (21 + 10) i.e., 31.

The sequence is –11, +9, –7, +5, –3, +1
So, 86 is wrong and should be replaced by (78 + 9) i.e., 87.

The sequence is +5, +7, ...... .
So, 24 is wrong and should be replaced by (17 + 9) i.e., 26.