# DIFFERENT PATTERNS OF NUMBER SERIES

Pattern 1:

When the difference between the consecutive numbers is same/ constant or the number series is in arithmetic progression.

a, a + d, a + 2d, a + 3d, a + 4d, …….., a + (n – 1)d.

Where a is first term, d is the common difference

Ex 1: 24, 21, 18, ?, 12, 9. Where the difference is -3, answer is 15

Pattern 2:

Any constant number is added to the difference of the consecutive numbers and form a series.

Ex 2: 2, 4, 8, 14, 22, 30 Next No. is 32 as 2 4 8 14 22 32 2 (2+2) (4+2) (6+2) (8+2)

Ex 3: 3, 4, 6, 9, 13, 18, __, Answer is 24 because 3 4 6 9 13 18 24 – 1 2 3 4 5 6

Pattern 3:

Multiplication or division Pattern When a series is multiplied or divide by certain constant.

Ex 4: 6174, 882, 126, ?. Answer is 18, the series is divisible by 7.

Ex 5: 1, 2, 3, 6, 9, 18, ?, 54 (a) 18 (b) 27 (c) 36 (d) 81 (e) None of these

Solution: The given series is in the pattern × 2, × 3/2, × 2, × 3/2, ×2,…..
So, the missing term is 18 × 3/2 = 27 Or
1 2 3 6 9 18 ? 54
+1 +1
1
+3 +3
1 × 3
+9 +9
3 × 3
+27
9 × 3
Ans: (b) 27
Pattern 4:

When a series follows the following pattern add, multiply, add, multiply, add,…. or add, substract, add,
substract, add,…. etc.
Ex 6: 4, 6, 12, 14, 28, 30, …..
Solution: 4 6 12 14 28 30 60
+2 ×2 +2 ×2 +2 ×2
60 is the next number
Ex 7: 8, 28, 116, 584, ? (R.R.B 2002)
(a) 1752 (b) 3502 (c) 3504
(d) 3508 (e) None of these
Solution: The given series is in the pattern: × 3 + 4, × 4 + 4, × 5 + 4, …..
(8 × 3) + 4 = 28
(28 × 4) + 4 = 116
(116 × 5) + 4 = 584
(584 × 6) + 4 = 3508
So, the missing term is 584 × 6 + 4 = 3508.
Ans: Option (d)
Ex 8: 3 4 10 33 136 685 ?
(a) 3430 (b) 4802 (c) 5145
(d) 4116 (e) 5488
Solution: In this particular Series, the pattern is-
3 × 1 + 1 = 4; 4 × 2 + 2 = 10; 10 × 3 + 3 = 33; 33 × 4 + 4 = 136; 136 × 5 + 5 = 685; 685 × 6 + 6 = 4116.
Hence option (d)
Pattern 5:

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Series with Square or cube or square root or cube root of the number.
Ex 9: 1, 9, 25, 49, ?, 121 (S.S.C.)
(a) 64 (b) 81 (c) 91
(d) 100 (e) None of these
Solution: The given series consists of squares of consecutive odd numbers i.e 12, 32, 52, 72,…..
So, the missing term = 92 = 81
Ans: Option (b)

Pattern 6: TRIANGULAR NUMBER
When any number series is in the form a, a + (a +1), a+ (a+1)+ (a+2), a + (a+1)+ (a+2) + (a+3), ………, nth term
of the series be

((n(n+1))/2)
Ex 10: 1, 3, 6, 4, 15, 21, …… find the 15th term of the series?
Solution : 15th term =
((n(n+1))/2) =(15×16)/2 =120

Pattern 7:

Product of the digits and summation with any constant, gives next number of the series.
Ex 11: 69, 55, 26, 13, 5 [Find the Wrong term of the Series]
(a) 69 (b) 55 (c) 26
(d) 13 (e) 5
Solution: We found that the series contains each term is one more than the product of the digits of the preceding term.
Thus (6 × 9 ) + 1 = 55, (5 × 5) + 1 = 26, (2 × 6 ) + 1 = 13, (1 × 3) + 1 = 4. Hence option (e).

Pattern 8:

Difference Between the adjacent numbers increases by a constant number.
Ex 12: 2, 7, 17, 32, ..?…….
(a) 42 (b) 52 (c) 47
(d) 27 (e) 62
Solution: In this particular series the gap between the numbers are 5, 10, 15, …so the next difference must be 20.
Than the next number be 52. Hence option (b)

Pattern 9:

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Percentage increasing and decreasing pattern
Ex 13: 105, 94.5, 103.95, 93.56, ..?…
(a) 102.91 (b) 102.98 (c) 102.95
(d) 103. 91 (e) none of these
Solution: In this particular Series the numbers are arranged on percentage increase and decrease pattern. As first there
is 10% decrease and than 10% increase..i.e 105 – 10% of 105 = 94.5, 94.5 + 10% of 94.5 = 103.95 ..and so on.
Hence option (a) 102.91 is the very next number of the series.
Pattern 10:

Division or Multiplication with increasing and decreasing numbers.

Ex 14: 16, 12, 18, 40.5, 121.5, 455.625 ?
(a) 2050.1125 (b) 2050.2125 (c) 2050.3125
(d) 2050.4125 (e) 2050.5125
Solution: The pattern of the above Series:
16 × 0.75 = 12, 12 × 1.5 (i.e 0.75 + 0.75 = 1.5) = 18, 18 × 2.25 (i.e 1.5 + 0.75 = 2.25) = 40.5, 40.5 × 3 (i.e 2.25 +0.75) = 121.5, ……, 455.625 × 4.50 = 2050.3125. Option (c)

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