# Number Series (Part-1)

Types of Number Series: Some of the important types of series are given below.

Addition Series: In this type of series, a number is added to the previous element to get the next element. The number which is added can be the same for the whole series or in a certain order.

Example(1): What will come in the place of question mark (?) in the given series?

2, 4, 6, 8, 10, ?

Answer: In the given series the difference between two consecutive elements is same. In this series, the number 2 is added in the previous element to get the next one. $$2 \overset{+2}{\longrightarrow}\ 4 \overset{+2}{\longrightarrow}\ 6 \overset{+2}{\longrightarrow}\ 8 \\ \overset{+2}{\longrightarrow}\ 10 \overset{+2}{\longrightarrow}\ \boxed{12}$$

Example(2): What will come in the place of question mark (?) in the given series?

1, 2, 4, 7, 11, ?

Answer: In the given series the difference between two consecutive elements is in the increasing order. In this series, the numbers 1, 2, 3, 4, and 5 are added to the previous element respectively, to get the next element in the increasing order. $$1 \overset{+1}{\longrightarrow}\ 2 \overset{+2}{\longrightarrow}\ 4 \overset{+3}{\longrightarrow}\ 7 \\ \overset{+4}{\longrightarrow}\ 11 \overset{+5}{\longrightarrow}\ \boxed{16}$$

Subtraction Series: In this type of series, a number is subtracted from the previous element to get the next element. The number which is subtracted can be the same for the whole series or in the increasing order.

Example(1): What will come in the place of question mark (?) in the given series?

16, 13, 10, 7, ?

Answer: In the given series the difference between two consecutive elements is same. In this series, the number 3 is subtracted from the previous element to get the next one. $$16 \overset{-3}{\longrightarrow}\ 13 \overset{-3}{\longrightarrow}\ 10 \overset{-3}{\longrightarrow}\ 7 \\ \overset{-3}{\longrightarrow}\ \boxed{4}$$

Example(2): What will come in the place of question mark (?) in the given series?

18, 17, 15, 12, ?

Answer: In the given series the difference between two consecutive elements is in the increasing order. In this series, the numbers 1, 2, 3, and 4 are subtracted from the previous element respectively, to get the next element in the increasing order. $$18 \overset{-1}{\longrightarrow}\ 17 \overset{-2}{\longrightarrow}\ 15 \overset{-3}{\longrightarrow}\ 12 \\ \overset{-4}{\longrightarrow}\ \boxed{8}$$