Test: Series - Class 5 MCQ

The rule followed is:
(3 x 3) + (4 x 4) = 9 + 16 = 25;
(9 x 9) + (10 x 10) = 81 + 100 = 181
So, (7 x 7) + (8 x 8) = 49 + 64 = 113

Given series: 13, 24, 46, 90, 178, ?.

24 – 13 = 11

46 – 24 = 22

90 – 46 = 44

178 – 90 = 88

The logic used here is that the difference between two successive numbers is doubled consecutively.

So, if 88 is doubled, we get 176.

Hence, 178 + 176 = 354.

Thus, the missing term in the sequence is 354.

So, the complete series is 13, 24, 46, 90, 178, 354.

The given sequence is obtained as follows:

2³ – 2² = 8 – 4 = 4

3³ – 3² = 27 – 9 = 18

4³ – 4² = 64 – 16 = 48

5³ – 5² = 125 – 25 = 100

6³ – 6² = 216 – 36 = 180

7³ – 7² = 343 – 49 = 294

8³ – 8² = 512 – 64 = 448

Hence, the missing number in the series is 48.

So, the complete series is 4, 18, 48, 100, 180, 294, 448.

2 + 3 + 6 + 9 = 20 
So, 20² = 400
1 + 4 + 9 + 13 = 27 
So,  27² = 729
9 + 8 + 11 + 2 = 30 
So, 30² = 900
So, the correct answer is 900

Given series: 1, 2, 10, 37, 101, ___.

1 + 1³ = 1 + 1 = 2

2 + 2³ = 2 + 8 = 10

10 + 3³ = 10 + 27 = 37

37 + 4³ = 37 + 64 = 101

101 + 5³ = 101+ 125 = 226

Thus, the given series follows a pattern of the sum of cubes of the consecutive natural numbers.

So, the complete series 1, 2, 10, 37, 101, 226.

Given series: 2, 3, 12, 37, 86, 166, 288.

2 + 1² = 2 + 1 = 3

3 + 3² = 3 + 9 = 12

12 + 5² = 12 + 25 = 37

37 + 7² = 37 + 49 = 86

86 + 9² = 86 + 81 = 167

167 + 11² = 167 + 121 = 288.

Here, the series follows a pattern of addition of the square of the consecutive odd numbers.

So, from the given number series 2, 3, 12, 37, 86, 166, 288, the wrong term is 166, because it should be 167.

Here, 5² = 25 and (5 + 1)² + 1 = 37

Similarly, 7² = 49 and (7 + 1)² + 1 = 65.

So, the missing number is 65.

The terms are given in a series:
(2³ - 1) = 7
(3³ - 1) = 26
(4³ - 1) = 63
(5³ - 1) = 124
(6³ - 1) = 215
(7³ - 1) = 342
So, the missing term is,
(8³ - 1) = 511.

The pattern is based on multiplying the previous term and then adding a number.
2 × 1 + 1 = 3
3 × 2 + 0 = 6
6 × 3 + 3 = 15
15 × 4 + 6 = 66

So, the next step: 5. 66 × 5 + 9 = 42 (This is the missing number).

Thus, the missing number in the series is 42.

Given series: 113, 225, 449, ? , 1793
113 x 2 = 226 -1 = 225
225 x 2 = 450 -1 = 449
449 x 2 = 898 - 1 = 897
897 x 2 = 1794 -1 = 1793
So, the correct answer is 897.