| 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. $$ 3 \overset{\times 2 \div 1}{\longrightarrow}\ 6 \overset{\times 3 \div 2}{\longrightarrow}\ 9 \overset{\times 4 \div 3}{\longrightarrow}\ 12 \\ \overset{\times 5 \div 4}{\longrightarrow}\ \boxed{15} $$