# Sequence and Series

Quantitative Aptitude Questions and Answers section on “Sequence, Series and Progression” with solution and explanation for competitive examinations such as CAT, MBA, SSC, Bank PO, Bank Clerical and other examinations.

1.

Find the missing number of the sequence:
“3, 14, 25, 36, 47, ?”
[A]1111
[B]1113
[C]1114
[D]None of these

None of these
$3\xrightarrow{+11}14\xrightarrow{+11}25\xrightarrow{+11}36\xrightarrow{+11}47\xrightarrow{+11}58$
∴ Missing number in the sequence = 58.
So option [D] is the right answer.

2.

The next term of the sequence 1, 2, 5, 26, … is:
[A]152
[B]677
[C]50
[D]47

677
The series is based on following pattern :
$\left ( 1 \right )^{2}+1=2$
$\left ( 2 \right )^{2}+1=5$
$\left ( 5 \right )^{2}+1=26$
$\left ( 26 \right )^{2}+1=677$
Therefore, the next number of this series will be 677.
Hence option [B] is correct.

3.

The missing term in the sequence 0, 3, 8, 15, 24, …, 48 is:
[A]30
[B]39
[C]35
[D]36

35
$0\xrightarrow{+3}3\xrightarrow{+5}8\xrightarrow{+7}15\xrightarrow{+9}24\xrightarrow{+11}35\xrightarrow{+13}48$
Missing no. = 35
Hence option [C] is the right answer.

4.

In the sequence of numbers 5, 8, 15, 20, 29, 40, 53, one number is wrong. The wrong number is :
[A]40
[B]20
[C]15
[D]29

15
$5\xrightarrow{+3}8\xrightarrow{+5}(13)15\xrightarrow{+7}20\xrightarrow{+9}29\xrightarrow{+11}40\xrightarrow{+13}53$
∴ Incorrect No. = 15
Hence option [C] is the right answer.

5.

1+2 + 3 + … + 49 + 50 + 49 + 48 + … + 3 + 2 + 1 is equal to:
[A]5000
[B]2525
[C]1250
[D]2500

2500
Required Sum =
$2\left ( \frac{x\left ( x+1 \right )}{2} \right )+50$
$=>\frac{2\times 49\times 50}{2}+50=2500$
Hence option [D] is the right answer.

6.

The next number of the sequence 3, 5, 9, 17, 33 …. is :
[A]49
[B]60
[C]65
[D]50

65
$3\xrightarrow{+2}5\xrightarrow{+4=2^{2}}9\xrightarrow{+8 = 2^{3}}17\xrightarrow{+16= 2^{4}}33\xrightarrow{+32 = 2^{5}}\underline{65}$
∴ The next term in the sequence will be 65.
Hence option [C] is the right answer.

7.

The next term of the sequence $\frac{1}{2}, 3\frac{1}{4}, 6, 8\frac{3}{4}, ...$ is :
[A]$10\frac{3}{4}$
[B]$11\frac{1}{2}$
[C]$10\frac{1}{4}$
[D]$11\frac{1}{4}$

$\mathbf{11\frac{1}{2}}$
Given sequence,
$\frac{1}{2}, 3\frac{1}{4}, 6, 8\frac{3}{4}, ...$
$= 0.5\xrightarrow{+2.75}3.25\xrightarrow{+2.75}6\xrightarrow{+2.75}8.75\xrightarrow{+2.75}\underline{11.5}$
∴ Next term of the sequence = 8.75 + 2.75 = 11.5 $= 11\frac{1}{2}$
Hence option [B] is the right answer.

8.

The next number in the sequence 2, 8, 18, 32, 50, …. is :
[A]80
[B]72
[C]68
[D]76

72
The given sequence is based on the following pattern :
$2\xrightarrow{+6}8\xrightarrow{+10}18\xrightarrow{+14}32\xrightarrow{+18}50\xrightarrow{+22}\underline{72}$
Hence, 72 will be the next number in this sequence.
Option [B] is the right answer.

9.

Next term of the sequence 8, 12, 9, 13, 10, 14, … is :
[A]17
[B]15
[C]11
[D]16

11
The pattern of the sequence is :
$8 + 4 = 12$
$12 - 3 = 9$
$9 + 4 = 13$
$13 - 3 = 10$
$10 + 4 = 14$
$14 - 3 = \underline{11}$
11 will be the next term in this sequence.

10.

The number of terms in the series 1 + 3 + 5 + 7 + …. + 73 + 75 is :
[A]30
[B]36
[C]38
[D]28

38
Let the number of terms be n.
It is an Arithmetic Series whose first term, a = 1 and common difference d = 2.
∴ nth term = a + (n – 1) d
$=> 75 = 1 + (n - 1) 2$
$=> 2 (n - 1) = 74$
$=> n - 1 = \frac{74}{2} = 37$
$=> n = 37 + 1 = 38$
Hence option [C] is the right answer.