## Number Series Questions and Answers Part-14

1. Find the missing term: 6, 18, 3, 21, 7, 56, ?
a) 8
b) 9
c) 63
d) 64

Explanation: 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 = 56 or x = 56 ÷ 7 = 8

2. Find the missing term: 1, 3, 4, 8, 15, 27, ?
a) 37
b) 44
c) 50
d) 55

Explanation: The sum of any three consecutive terms of the series gives the next term,
So, missing number = 8 + 15 + 27 = 50

3. Find the missing term: 20, 20, 19, 16, 17, 13, 14, 11, ?, ?
a) 10, 10
b) 10, 11
c) 13, 14
d) 13, 16

Explanation: Let the missing terms of the series be x1 and x2.
Thus, the sequence 20, 20, 19, 16, 17, 13, 14, 11. x1, x2 is a combination of two series:
I. 20, 19, 17, 14, x1 and
II. 20, 16, 13, 11, x2
The pattern in I is - 1, - 2, - 3,..............So, missing term, x1= 14 - 4 = 10
The pattern in II is - 4, - 3, - 2,.......... So,missing term, x2 = 11 - 1 = 10

4. Find the missing term: 45, 54, 47, ?, 49, 56, 51, 57, 53
a) 48
b) 50
c) 55
d) None of these

Explanation: 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.

5.Find the missing term: 2, 15, 4, 12, 6, 7, ?, ?
a) 8, 8
b) 8, 0
c) 3, 8
d) None of these

Explanation: Let the missing terms of the series be x1 and x2.
Thus, the sequence 2, 15, 4, 12, 6, 7, x1, x2 is a combination of two series:
I. 2, 4, 6, x1 and
II. 15, 12, 7, x2
I consists of consecutive even numbers. So, missing term, x1= 8
The pattern in II is - 3, - 5, ........So, missing term x2 = 7 - 7 = 0

6. Find the missing number: 111/9, 121/2, 142/7, 162/3, ?
a) 81/3
b) 191/2
c) 20
d) 221/3

Explanation: The given sequence is 100/9 , 25/2 , 100/7 , 50/3, ............i.e., 100/9, 100/8, 100/7, 100/6.................
So, missing term = 100/5 = 20

7. Find the missing term: 8, 9, 8, 7, 10, 9, 6, 11, 10, ?, 12
a) 5
b) 7
c) 8
d) 11

Explanation: The given sequence is a combination of three series:
I. 1st, 4th, 7th, 10th, terms i.e., 8, 7, 6, ?
II. 2nd, 5th, 8th, 11th terms i.e.,9, 10, 11, 12
III. 3rd, 6th, 9th, terms i.e., 8, 9, 10
The pattern in I. is - 1 So, the missing term is = 6 - 1 = 5

8. Which term of the series 5, 8, 11, 14, ....is 320 ?
a) 104th
b) 105th
c) 106th
d) 64th

Explanation: Clearly, 5 + 3 = 8, 8 + 3 = 11, 11 + 3 = 14,................
So, the series in an A.P. in which a = 5 and d = 3
Let 320 be the nth term of the series.
Then, 320 = 5 + (n - 1) × 3 or (n - 1) = 105 or n = 106

9. Find the missing term: 1, 9, 25, 49, ?, 121
a) 64
b) 81
c) 91
d) 100