As we know, questions related to number series are very important in Quantitative aptitude section, So, today I'm going to discuss some problems of number series. These are just for your practice. I have already discussed this chapter in previous session i.e. Sequence and Series. Read this article first, then go through these examples.
Examples with Solutions
Example1: In the following given series, find out the wrong number.
`1, 3, 10, 21, 64, 129, 356`
Solution: As i have discussed in previous session, operations applied on series can be: Addition or subtraction, multiplication or division, squaring or cubing and combination of any.
Series `1 3 10 21 64 129 356`
Difference ` 2 7 11 43 65 227`
By studying the above series, you'll come to know that, this is a combination of operations. Operation used is discussed as follows:
Alternately using: (`times 2 + 1`) and (`times 3 + 1`)
`1 times 2 + 1 = 3`
`3 times 3 + 1 = 10`
`10 times 2 + 1 = 21`
`21 times 3 + 1 = 64`
`64 times 2 + 1 = 129`
`129 times 3 + 1 = 388`
Therefore, last number of series is wrong i.e.`356`
Example2: Find the next number of the following series:
`672, 560, 448, 336, 224,?`
Solution: Check out the difference of each number first:
Series: `672 560 448 336 224`
Difference: `112 112 112 112`
Difference between all the terms is same i.e. `112`
Therefore, next term will be = `224 - 112` = `112` Ans
Example3: Find the next term of following series:
`82, 67, 54, 43, 34`
Solution: The operation used in series is discussed as follow:
`9^2 + 1` = `82`
`8^2 + 3` = `67`
`7^2 + 5` = `54`
`6^2 + 7` = `43`
`5^2 + 9` = `34`
Continuing like this;
`4^2 + 11` = `27`
Therefore, `27` is the next term.
Example4: What should come in place of question mark?
`1721, 2190, 2737, 3368,?`
Solution: As we can see, first term is approximately equal to the cube of `12`, so firstly we will try to solve it with the cubes.
`(12)^3 - 7` = `1721`
`(13)^3 - 7` = `2190`
`(14)^3 - 7` = `2737`
`(15)^3 - 7` = `3368`
Now you can find, that there is some pattern. So, continuing like this, we get
`(16)^3 - 7` = `4089` Ans
Example5: Find the next term of following series:
`8, 24, 12, 36, 18, ?`
Solution: Relation between the terms is as follows:
`8 times 3= 24`
`(24/2) = 12`
`12 times 3=36`
`(36)/2=18`
Continuing like this:
`18 times 3 = 54`
Therefore, next term is `54`
Example 6: Find the next term of the following series:
`47, 33, 21, 11, ?`
Solution: The pattern used in the series is as follows:
`7^2 - 2 = 47`
`6^2 - 3 = 33`
`5^2 - 4 = 21`
`4^2 - 5 = 11`
By continuing, we get
`3^2 - 6 = 3`
Therefore, `3` is the next term.
I will soon update the questions for your practice.
