# Number Series (Part-3):

#### Overview:

 Topic Included: Definitions & Exmaples. Main Topic: Verbal Reasoning. Verbal Reasoning Sub-topic: Number Series Notes and Questions. Questions for practice: Questions & Answers included.

Mixed Series: In this type of series more than one mathematical processes are used in the same time. Some of the mixed series are given below.

Multiplication and Addition Series: In this type of series, a number $$x_1$$ is multiplied and another number $$x_2$$ is added with the previous element at the same time, to get the next element.

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

2, 4, 10, 32, ?

Answer: Here the previous element is multiplied by 1, 2, 3 and 4 in increasing order but at the same time, the previous element is added by number 2 also to get the next element. $$2 \overset{\times 1 +2}{\longrightarrow}\ 4 \overset{\times 2 +2}{\longrightarrow}\ 10 \overset{\times 3 +2}{\longrightarrow}\ 32 \\ \overset{\times 4 +2}{\longrightarrow}\ \boxed{130}$$

Multiplication and Subtraction Series: In this type of series, a number $$x_1$$ is multiplied and another number $$x_2$$ is subtracted with the previous element at the same time, to get the next element.

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

3, 2, 2, 3, ?

Answer: Here. the previous element is multiplied as well as subtracted by the numbers 1, 2, 3 and 4 at the same time. $$3 \overset{\times 1 -1}{\longrightarrow}\ 2 \overset{\times 2 -2}{\longrightarrow}\ 2 \overset{\times 3 -3}{\longrightarrow}\ 3 \\ \overset{\times 4 -4}{\longrightarrow}\ \boxed{8}$$

Multiplication and Division Series: In this type of series, a number $$x_1$$ is multiplied and another number $$x_2$$ is divided with the previous element at the same time, to get the next element.

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

3, 6, 9, 12, ?

Answer: Here the previous element is multiplied by 2, 3, 4 and 5 in increasing order and at the same time, the previous element is divided by the numbers 1, 2, 3 and 4 in increasing order. $$3 \overset{\times 2 \div 1}{\longrightarrow}\ 6 \overset{\times 3 \div 2}{\longrightarrow}\ 9 \overset{\times 4 \div 3}{\longrightarrow}\ 12 \\ \overset{\times 5 \div 4}{\longrightarrow}\ \boxed{15}$$