Number

Tips and Tricks – Perfect Square Series

Consists of the perfect square of some numbers arranged in a specific order, with one number missing. Now we’ve to find the pattern the series is following and fill up the blank accordingly by finding that number.

Question 1.

100,121,144,__, 196

Solution:

This series consists of a perfect square of consecutive numbers 10, 11, 12, 13

Hence 169 will come in the blank.

Tips and Tricks – Perfect Cube Series

It consists of a cube of numbers sequenced in a particular order.

Question 1.

9,64, 125, __, 343

Solution:

This series consists of a series of numbers with perfect cubes the is (3 x 3 x 3), (4 x 4 x 4), (5 x 5 x 5), (6 x 6 x 6), (7 x 7 x 7)

Hence 216 will be coming in the blank, as the series is following a trend of cubes of numbers in sequential order.

Tips and Tricks and Shortcuts- Ration Series

This type of series consists of numbers arranged in sequential order (following a particular trend, i.e., Either increasing or decreasing). Now, all we have to do here is to trace out this trend,(which could be *, /, +, -) of each number of the series with a fixed number) by finding the proportional difference between the numbers of the series.

Question 1.

3, 6, 9, 12, __, 18, 21

Solution:

Here the series is following an increasing trend in which three is added to each number of the series.

3

6 (3+3)

9 (6+3)

12 (9+3)

15 (12+3)

18 (15+3)

21 (18+3)

Tips and Tricks and Shortcuts – Arithmetic series

In this kind of sequences, each number is found by ( + , -) each term by a constant number.

The formula of  A S = {a, a+d, a +2d.….}

Where a= first term of the series

d = common difference

Question 1.

3, 6, 9 , 12

Solution:

Here a = 3(first term of the series)

d = 3

Hence we get:

3 + 3 = 6

6 + 3 = 9

9 + 3 = 12

12 + 3 = 15

Tips and Tricks and Shortcuts – Geometric series

In this kind of sequences, each number is found by (*, /) each term by a constant number.

The formula of G S= {a, ar, ar², ar³,….}

Where a= first term of the series

R= factor or difference between the term, also known as the common ratio.

Question 1.

1, 2, 4, 8, 16, 32

Solution:

Here a = 1 (first term of the series)

r = 2 (a standard number that is multiplied with the consecutive number of the series)

Hence we get:

1

1 x 2

1 x 2²

1 x 2³, ….)

Tips and Tricks and Shortcuts – Mixed series

In such series, while calculating the difference, there can be two steps involved in getting the next consecutive number of the series. So we’ve to follow the same pattern to get the perpetual number of the series.

Question 1.

$1, \frac{5}{2}, \frac{10}{3}, \frac{17}{4}, —$

Options:

A.  $\frac{26}{5}$

B.  $\frac{24}{5}$

C.  $\frac{21}{5}$

D.  5

Correct Option: A

Explanation:

Here we’ve to observe the trend that this series is following, as each term is divided by a specific number, i.e., 1 then 2 then3 then 4 and so on. Hence we can make out that the denominator must be 5.

Now comes the numerator, where the 1’st number is 1.

Then comes 5, now how can we get 5 from the term number 2. It can come by $\frac{2^{2} + 1 }{2} = \frac{5}{2}$ Next comes $\frac{3^{2} + 1 }{3} = \frac{10}{3}$,$\frac{4^{2} + 1 }{4} = \frac{17}{4}$, $\frac{5^{2} + 1 }{5} = \frac{26}{5}$ 

Hence option A is the correct one.