Series
Series
Number Series
In number series problems we have to find the relation between the successive terms or the pattern
in the terms of the series.
For this, we have to be familiar with numbers and able to express numbers in different ways.
For example, 29 = 30 - 1 = 7 ⨯ 4 + 1 = 52 + 22 = 33 + 2 = 5 ⨯ 4 + 32 = . . . .
Familiarity with numbers in these ways can help to get answers quickly for the number series problems.
1. The next term in the series is : 2, 5, 9, 19, 37, ? (1)75 (2)78 (3)80 (4)73
5 = 2 + 3, 9 = 5 + 4 (4 = 3 + 1). The next term has to be 9 + 5 = 14 (5 = 4 + 1).
But the next term is 19. So this is not the pattern of the given series.
We can observe that the terms are nearly double the previous term.
5 = 2 × 2 + 1 and 5 × 2 + 1 = 11. But the next term = 9 = 5 × 2 - 1.
So alternatively we have to add 1 (+ 1) and subtract 1 (- 1).
And the term after 9 is 9 × 2 + 1 = 19, then 19 × 2 - 1 = 37.
So the next term is 37 × 2 + 1 = 75. Ans. 1.
In short, the given series is 2, 2 × 2 + 1, 5 × 2 - 1, 9 × 2 + 1, 19 × 2 - 1.
So the next term is 37 × 2 + 1 = 75.
2. Find the missing number in the following: 4242, 4254, 4230, 4266, 4218, 4278, ---------
(a) 4264 (b) 4272 (c) 4228 (d) 4206
Observe that the given series terms are increasing and decreasing alternatively. Yes,
4254 = 4212 + 12, 4230 = 4254 - 24, 4266 = 4230 + 36, 4218 = 4266 - 48 and 4278 = 4218 + 60.
First add 12, next subtract 24 = 2 × 12, next add 36 = 3 × 12, next subtract 48 = 4 × 12, next add 60 = 5 × 12. So, next we have to subtract 6 × 12 = 72 from 4278.
And the missing number is 4278 - 72 = 4206. Ans. d.
In short we write this as follows:
4242, 4254, 4230, 4266, 4218, 4278,
+12 -24 +36 -48 +60 -72 4278 - 72 = 4206
Here after we write the solutions to the problems in short.
3. Find the next number in the sequence : 1, 7, 33, 159, 785, … .
(a)944 (b)1570 (c)3911 (d)626
1, 7, 33, 159, 785, …..
+ 6 +26 +126 +626 Think and find the pattern in 6, 26, 126, 626. Yes 6 = 5+1, 26 = 52+1
5+1 52+1 53+1 54+1 55+1 = 3125+1 = 3126 785 + 3126 = 3911
4. The next term in the series : 2, 7, 28, 63,126,------- is (1)215 (2) 245 (3) 276 (4) 296
13 + 1, 23 - 1, 33 + 1, 43 - 1, 53 + 1, 63 - 1 = 216 - 1 = 215
5. The next number in the series 1, 16, 81, 256 is a)738 b) 464 c) 625 d) 525
12, 42, 92, 162,
4 = 1+3, 9 = 4+5, 16 = 9+7. So next 16+9 and we have to square it.
(16+9)2 = 252= 625
6. The next term in the series 2, 5, 10, 17, 26, 37, ---?--- is : (1) 50 (2) 57 (3) 62 (4) 72
2, 2+3, 5+5, 10+7, 17+9, 26+11, 37+13 = 50
7. In the series 3, 11, 23, 39, 59,------ the next term will be (1) 63 (2) 73 (3) 83 (4) 93
+ 8 12 16 20 24 and 59+24 = 83
Directions (8 - 12): What will come in the place of ? mark in the following number series.
8. 200, 193, 179, 158, ?, 95 (a) 135 (b) 133 (c) 132 (d) 130 (e) 128
200, 193, 179, 158, ?, 95
-7, -14, -21, -28, -35 And ? = 158 - 28 = 130, 130 - 35 = 95
9. 3, 43, 81, 115, 143, ? (a) 163 (b) 172 (c) 166 (d) 160 (e) 168
3, 3+40, 43+38, 81+34, 115+28, ? = 143+20 = 163
38 = 40 - 2, 34 = 38 - 4, 28 = 34 - 6. So next 28 - 8 = 20
10. 1, 6, 25, 76, 153, ? (a) 152 (b) 154 (c) 153 (d) 155 (e) 156
1, 6, 25, 76, 153, ?
1 × 5 + 1, 6 × 4 + 1, 25 × 3 + 1, 76 × 2 + 1, ? = 153 × 1 + 1 = 154
11. 50, 54, 45, 61, 36, ? (a) 66 (b) 72 (c) 75 (d) 80 (e) 84
50, 54, 45, 61, 36, ?
+4, - 9, +16, - 25, +!
+22 - 32 + 42 - 52 +62 = 36 And ? = 36 + 36 = 72
12. 9, 45, 180, 540, ?, 1080 (a) 720 (b) 900 (c) 1080 (d) 1200 (e) 960
9, 45, 180, 540, ?, 1080
9×5, 45×4, 180×3, 540×2, 1080×1 ? = 540 × 2 = 1080
Directions (13 – 15): In each of the following questions a number series is given in which
one number is wrong. You have to find out that number and have to follow the new series
which will be started by that number.
Then what will be the third number of the new series?
13. 2 9 5 36 125 648 3861 (a) 13 (b) 61 (c) 75 (d) 72
The given series increases except the third term. So from the answer choices the wrong one is
not 125, 648, 3861. We observe that the 6th term 648 is more than 5 times of the 5th term 125,
but the 7th term 3861 is less than 6 times of the 6th term 648. Infact, 648 = 125 × 5 + 23,
3861 = 648 × 6 - 27 and 27 - 23 = 4. So the 2nd term 9 is one time more than the 1st term 2.
And 9 = 2 × 1 + 7. So the 3rd term is less than 2 times the 2nd term 9 by 7 + 4 = 1(since 27-23 =4)
We verify whether the other terms are in this pattern.
2, 9 = 2 × 1 + 7, 9 × 2 -11 = 7, 7 × 3 + 15 = 36, 125 = 36 × 4 - 19, 648 = 125 × 5 + 23,
3861 = 648 × 6 - 27
7 is wrongly given as 5
Starting with 5 the new series is 5, 5 × 1 + 7 = 12, 12 × 2 - 11 = 13 Ans (a)
14. 3 4 12 45 190 1005 6066 (a) 98 (b) 96 (c) 384 (d) 386
3, 3 × 1 + 1 = 4, 4 × 2 + 22 = 12, 12 × 3 + 32 = 45, 45 × 4 + 42 = 196, 196 × 5 + 52 = 1005,
1005 × 6 + 62 = 6030 + 36 = 6066
190 is the wrong one
Starting with 190 the new series is 190, 190 × 1 + 1 = 191, 191 × 2 + 22 = 386 Ans. (d)
15. 2 7 19 43 99 209 431 (a) 181 (b) 183 (c) 87 (d) 85
2, 2 × 2 + 3 = 7, 7 × 2 + 5 = 19, 19 × 2 + 7 = 45, 45 × 2 + 9 = 99, 99 × 2 + 11 = 209,
209 × 2 + 13 = 431
43 is wrong
Starting with 43 the new series is 43, 43 × 2 + 3 = 89, 89 × 2 + 5 = 183. Ans. (b)
Directions (16 – 18): In each of the following questions a number series is given.
After the series, a number is given followed by (a), (b), (c), (d) and (e).
You have to complete the series starting with the number given,
following the sequence of the given series.
16. 2 10 27 60
5 (a) (b) (c) (d) (e)
Which of the following numbers will come in place of (b)? (a) 39 (b) 13 (c) 34 (d) 38
2, 2 × 2 + 6 = 10, 10 × 2 + 7 = 27, 27 × 2 + 6 = 60
5, a = 5 × 2 + 6 = 16, b = 16 × 2 + 7 = 39. Ans (a)
17. 15 16 25 50
189 (a) (b) (c) (d) (e)
Which of the following numbers will come in place of (e)? (a) 354 (b) 273 (c) 394 (d) 426
15, 15 + 1 = 16, 16 + 32 = 25, 25 + 52 = 50
189, a = 189 + 1 = 190, b = 190 + 32 = 199, c = 199 + 52 = 224, d = 224 + 49 = 273,
e = 273 + 81 = 354. Ans. (a)
18. 5 149 49 113
146 (a) (b) (c) (d) (e)
Which of the following numbers will come in place of (d)? (a) 290 (b) 234 (c) 254 (d) 218
5, 5 + 144 = 149, 149 - 100 = 49, 49 + 64 = 113
+122 -102 +82 -62 = -36
146, a = 146 + 144 = 290, b = 290 - 100 = 190, c = 190 + 64 = 254, d = 254 - 36 = 218. Ans. (d)
19. The next term in the sequence 0, 2, 24, 252, 3120 , …. is
42450 B. 46650 C. 38450 D. 44650 E. Answer not known
0 = 1 - 1, 2 = 22 - 2, 24 = 33 - 3, 252 = = 44- 4, 3120 = 55 - 5,
… = 66- 6 = 46656 - 6 = 46650
20. Find out the wrong number in the sequence. 623, 251, 543, 356.
(a)543 (b)251 (c)623 (d)356
251 is prime but all the other numbers are composite
21. Find out the wrong number in the sequence. 121, 264, 312, 462, 583.
(a)583 (b)264 (c)462 (d)312
312 is not a multiple of 11, but the others are multiple of 11
22.Find out the odd number in the series 25, 36, 49, 81,121,169, 225. (a)36 (b)49 (c)169 (d)225
36 is the only even number
23. Find the odd man out in the following: 1, 144, 16, 25, 49, 81, 121, 36, 62
(a) 1 (b)49 (c)121 (d)62
62 is not a perfect square, but all the others are perfect square
Series Like Number Figure Problems
24. Find the missing number in the place?
(a)10 (b)11 (c)13 (d)14
In each figure one number is in the centre.
To find out the pattern, we express the centre number in terms of the other four numbers.
(6 ÷ 2) + (8 ÷ 4) = 5; (12 ÷ 3) + (20 ÷ 5) = 8;
? = (20 ÷ 2) + (36 ÷ 9) = 14
25. Find the missing number in the place ?
In each figure the number in the top is larger than the other two
in the bottom. To find out the pattern, we express the larger one in terms of the other two.
5 = 12+22; 13 = 22+32; 25 = 32+42;
? = 42+52 = 41
26. Find the missing number
In each quadrant the number in the inner rectangle is larger than the other two.
To find out the pattern, we express the larger one in terms of the other two.
9 = (1 + 2)(12 + 2),
35 = (2 + 3)(22 + 3),
91 = (3 + 4)(32 + 4),
? = (4 + 5)(42 + 5) = 189
(a)18 (b)19 (c)20 (d)21
1 × 2 - 1 = 1, 2 × 3 - 1 = 5, 3 × 4 - 1 = 11
? = 4 × 5 - 1 = 19
28. Find the missing term
(a)12 (b)18 (c)16 (d)24
5 × 4 + 2 × 3 = 26, 4 × 8 + 5 × 2 = 42, 3 × ? + 8 × 1 = 44. ? = 12
29. What is the value of X in Fig. II?
30. Find x in
(a)4 (b)7 (c)9 (d)3
84 = 5 × 6 + 9 × 6; 70 = 7 × 7 + 3 × 7;
56 = 8 × 4 + 6 × 4; 36 = 5 × 3 + 3 × x
x = 7
31.
(d)
32. What will come in the place of a question mark?
(a)9 (b)6 (c)7 (d)3
W is the third letter from T; S is the 15th letter from D; T is the tenth letter from J;
P is the 9th letter from G (a)
Alphabet Series
33. Find the next alphabet in the sequence B, E, I, N, ? (a)U (b)V (c)T (d)S
B CD E FGH I JKLM N OPQRS T Ans. c.
34.Find the missing letters in the series AZ, GT, MN, ??, YB.
(a)JH (b)SH (c)SK (d)TS
A G M 5 letters in between A and G, and between G and M. A BCDEF G, G HIJKL M.
So, M NOPQR S and S TUVWX Y.
Z T N 5 letters in reverse order in between each, Z YXWVU T, T SRQPO N.
So, N MLKJI H
Ans. b. SH
35. The next term in the series : BA, ED, IH, NM,------ is (1)TS (2) ST (3) TU (4) SU
B D 1 letter in between B and D and the next letter is E
E H 2 letters in between E and H and the next letter is I
I M 3 letters in between I and M and the next letter is N
N * ? 4 letters between N and ? and * is the next letter to ?
So ? is S and the next letter * is T. Ans. 1. TS
36. The next term in the series : B2E, D5H, F12K, H27N, ----?--- is :
1)J56I (2)I62Q (3)Q62J (4)J58Q
B D F H one letter in between each, so the answer begin with J
2 5 = 2 × 2 + 1, 12 = 2 × 5 + 2, 27 = 2 × 12 + 3, next = 2 × 27 + 4 = 58, only one choice is given with J58. So, the answer is (4)
Of course you can verify that the last letter is Q
(2 letters between N and Q)
37. In the series AB, EDC,FGHI,---?---, OPQRST, the missing term is
(1) JKLMN (2) JMKNL (3) NMLKJ (4) NMKLJ
First two letters, next three letters in reverse order, next 4 letters,
next five letters in reverse order = NMLKJ, next 6 letters OPQRST. Ans. (3)
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