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1.

7, 26, 63, 124, 215, 342, ?

Answer» The terms of the given series are (23 - 1), (33 - 1), (43 - 1), (53 - 1), (63 - 1), (73 - 1),..... So, missing term = (83 - 1) = (512 - 1) = 511.
2.

3, 12,27,48, 75, 108,?

Answer» The terms of the given series are 3 x l2, 3 x 22, 3 x 32, 3 x 42, 3 x 52, 3 x 62,..... So, missing term = 3 x 72 = 3 x 49 = 147.
3.

3, 7, 23, 95, ?

Answer» The pattern is x 2 + 1, x 3 + 2, x 4 + 3,..... So, missing term = 95 x 5 + 4 = 479.
4.

6, 18, 3, 21, 7, 56, ?

Answer» Each term at an even place in the series is the product of its two adjacent terms. Thus, if the missing term be x, then we have : 7 x x = 56 or x = 56 ÷ 7 = 8.
5.

4, 9, 25, ?, 121, 169, 289, 361

Answer» The given series consists of squares of consecutive prime numbers i.e. 22, 32, 52,....., 112, 132, 172, 192. So, missing term = 72 = 49.
6.

45, 54, 47, ?, 49, 56, 51, 57, 53

Answer» The given sequence is a combination of two series: I. 45, 47, 49, 51, 53 and II. 54, ?, 56, 57 Clearly, II consists of consecutive natural numbers, starting from 54. So, missing term = 55.
7.

3, 8, 13, 24, 41, ?

Answer» The pattern followed is : nth term + (n + l)th term + (n + 1) = (n + 2)th term. Thus, 1st term + 2nd term + 2 = 3rd term; 2nd term + 3rd term + 3 = 4th term and so on. So, missing term = 6th term = 4th term + 5th term + 5 = 24 + 41 + 5 = 70.
8.

10, 14, 26, 42, 70, ?

Answer» Each term in the series, except the first two terms, is 2 more than the sum of the preceding two terms. So, missing term = (42 + 70) + 2 = 114.
9.

1, 2, 6, 7, 21, 22, 66, 67, ?

Answer» The pattern is + 1, x 3, + 1, x 3, + 1, x 3, + 1,..... So, missing term = 67 x 3 = 201.
10.

0.5, 0.55, 0.65,0.8,?

Answer» The pattern is + 0.05, + 0.10, + 0.15,..... So, missing term = 0.8 + 0.20 = 1.
11.

0, 2, 3, 5, 8, 10, 15, 17, 24, 26, ?

Answer» The given sequence is a combination of two series : I. 0, 3, 8, 15, 24, ? and II. 2, 5, 10, 17, 26 The pattern in each one of I and II is + 3, + 5, + 7, + 9, ..... So, missing term = 24 + 11 = 35.
12.

11, 13, 17, 19, 23, 25, ?

Answer» The pattern is + 2, + 4, + 2, + 4, ..... So, missing term = 25 + 4 = 29.
13.

5, 2, 7, 9, 16, 25, ?

Answer» Each term in the series, except the first two terms, is the sum of the preceding two terms. So, missing term = 16 + 25 = 41.
14.

24576, 6144, 1536, 386, 96, 24

Answer» Each term of the series is obtained by dividing the preceding term by 4. So, 1536 is wrong and must be replaced by (1536 + 4) i.e. 384.
15.

10, 14, 28, 32, 64, 68, 132

Answer» The correct pattern is + 4, x 2, + 4, x 2, ..... So, 132 is wrong and must be replaced by (68 x 2) i.e. 136.
16.

89, 78, 86, 80, 85, 82, 83

Answer» The correct pattern is - 11, + 9, - 7, + 5, - 3, + 1. So, 86 is wrong and must be replaced by (78 + 9) i.e. 87.
17.

0, 2, 3, 5, 8, 10, 15, 18, 24, 26, 35

Answer» The given sequence is a combination of two series: I. 0, 3, 8, 15, 24, 35 and II. 2, 5, 10, 18, 26 The pattern in both I and II is + 3, + 5, + 7, + 9,..... So, in II, 18 is wrong and must be replaced by (10 + 7) i.e. 17.
18.

325, 259, 202, 160, 127, 105, 94

Answer» The correct pattern is - 66, - 55, - 44, - 33, - 22, - 11. So, 202 is wrong and must be replaced by (259 - 55) i.e. 204.
19.

1236, 2346, 3456, 4566, 5686

Answer» The correct pattern in the series is + 1110. So, 5686 is wrong and must be replaced by (4566 + 1110) i.e. 5676.
20.

93, 309, 434, 498, 521, 533

Answer» The correct pattern is + 63, + 53, + 43, + 33, ..... So, 521 is wrong and must be replaced by (498 + 33) i.e. 525.
21.

105, 85, 60, 30, 0, - 45, - 90

Answer» The correct pattern is - 20, - 25, - 30,..... So, 0 is wrong and must be replaced by (30 - 35) i.e. - 5.
22.

125, 126, 124, 127, 123, 129

Answer» The correct pattern is + 1, - 2, + 3, - 4, + 5. So, 129 is wrong and must be replaced by (123 + 5) i.e. 128.
23.

ADVENTURE, DVENTURE, DVENTUR, ?, VENTU

Answer» One letter from the beginning and one from the end of a term are removed, one by one, in alternate steps.
24.

A, D, H, M, ?, Z

Answer»
25.

PERPENDICULAR, ERPENDICULA, RPENDICUL, ?

Answer» Each term of the series is obtained by removing two letters from the preceding term one from the beginning and one from the end, So, the missing term is PENDICU.
26.

Z, ?, T, ?, N, ?, H, ?, B

Answer»
27.

ejo tyd ins xch ?

Answer» There is a gap of four letters between the first and second, the second and third letters of each term, and also between the last letter of a term and the first letter of the next term.
28.

A, B, N, C, D, O, E, F, P, ?, ?, ?

Answer» The given series may be divided into 2 groups : I. A, B, C, D, E, F, ?, ? and II. N, O, P, ? Clearly, the given series consists of two terms of I followed by one term of II. The missing terms in I are G and H while the missing term in II is Q.
29.

GH, JL, NQ, SW, YD, ?

Answer»
30.

R, U, X, A, D, ?

Answer»
31.

AYD, BVF, DRH, ?, KGL

Answer»
32.

AZ, CX, FU, ?

Answer»
33.

A, B, B, D, C, F, D; H, E, ?, ?

Answer» The given sequence is a combination of two series : I. 1st, 3rd, 5th, 7th, 9th, 11th terms i.e. A, B, C, D, E, ? II. 2nd, 4th, 6th, 8th, 10th terms i.e. B, D, F, H, ? Clearly, I consists of consecutive letters while II consists of alternate letters. So, the missing letter in I is F, while that in II is J. So, the missing terms i.e. 10th and 11th terms are J and F respectively.
34.

Z, X, S, I, R, R, ?, ?

Answer» Note that the numbers representing the difference between the consecutive terms of the series again from a series - 2, 5, 10, 17, 26, 37, 50 - in which the pattern is +3, +5, +7, +9, +11, +13.
35.

AYBZC, DWEXF, GUHVI, JSKTL, ?

Answer»
36.

T, R, P, N, L, ?, ?

Answer»
37.

PMT, OOS, NQR, MSQ, ?

Answer»
38.

Z, U, Q, ?, L

Answer»
39.

M, N, O, L, R, I, V, ?

Answer» The given sequence is a combination of two series: I. M, O, R, V and II. N, L, I, ?
40.

B, D, F, I, L, P, ?

Answer»
41.

ATTRIBUTION, TTRIBUTIO, RIBUTIO, IBUTI, ?

Answer» In the first step, one letter from the beginning and one from the end of a term are removed to give the next term. In the second step, two letters from the beginning of a term are removed. These two steps are repeated alternately.
42.

DHL, PTX, BFJ, ?

Answer»
43.

A, CD, GHI, ?, UVWXY

Answer» Each term consists of consecutive letters in order. The number of letters in the terms goes on increasing by one at each step. Also, there is a gap of one letter between the last letter of the first term and the first letter of the second term; a gap of two letters between the last letter of the second term and the first letter of the third term; and so on. So, there should be a gap of three letters between the last letter of the third term and the first letter of the desired term.
44.

Z, Y, X, U, T, S, P, O, N, K, ?, ?

Answer»
45.

U, B, I, P, W, ?

Answer»
46.

AI, BJ, CK, ?

Answer»
47.

A, G, L, P, S, ?

Answer»
48.

ajs, gpy, ?, sbk, yhq

Answer»
49.

AB, DEF, HIJK, ?, STUVWX

Answer» The number of letters in the terms of the given series increases by one at each step. The first letter of each term is two steps ahead of the last letter of the preceding term. However, each term consists of consecutive letters in order.
50.

Y, B, T, G, O, ?

Answer» The given sequence is a combination of two series : I. Y,T, O and II. B, G, ? I consists of 2nd, 7th and 12th letters from the end of the English alphabet, while II consists of 2nd, 7th and 12th letters from the beginning of the English alphabet. So, the missing letter in II is the 12th letter from the beginning of the English alphabet, which is L.