Number Series Involving Difference
Number Series Involving Difference
Number Series:
It consists of questions in which series of numbers are given, which are generally called the terms of the series. These terms follow a certain pattern throughout the series.The candidate is required to study the given series, identify the patterns followed in the series and either complete the given series with the most suitable alternative or find the wrong term in the series.
Before stating with number series, it is important to know about numbers.
Whole Numbers : 0,1,2,3,4,5............
Natural Numbers : 1, 2, 3, 4, 5, 6, 7, 8..........
Even Numbers : 2, 4, 6, 8, 10........
Odd Numbers : 1, 3, 5 , 7, 9, 11...........
Prime Numbers : Have 2 factors only. e.g. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31............
Composite Numbers : Have more than 2 factors. 4, 6, 8, 9, 10, 12.............
Case I: Completing The Given Series By Finding The Missing Term(s)
Illustration: Find the next term in the series: 3, 7, 11, 15, ___
(a) 21 (b) 23 (c) 17 (d) 19
Solution: To Analyse the series we will find the difference between the two terms
7 - 3 = 4, 11 - 7 = 4 , 15 - 11= 4
Clearly, the given sequence follows the pattern : + 4
So the Next Term will be 15 + 4= 19
Answer is: (d)
Sometimes, the difference between the consecutive terms of a series, again form a series. The difference between the consecutive terms of the new series so formed, again form a series. This pattern continues till we attain a uniform difference between the consecutive terms of the series.
Illustration: FInd the missing term in each of the following series:1, 6, 15, ___, 45, 66, 91
(a) 25 (b) 26 (c) 27 (d) 28
Solution: To Analyse the series we will find the difference between the two terms
6 - 1 = 5, 15 - 6 = 9, _______ , _______, 66 - 45 = 21, 91 - 66 = 25
Clearly, the given sequence follows the pattern : + 5, + 9, + 13, + 17, + 21, + 25,......
So, missing term = 15 + 13 = 28. and further 28 + 17 = 45
Answer: Hence, the answer is (d).
Illustration: Find the missing term in the series : 3, 20, 63, 144, 275,?
(a) 354 (b) 468 (c) 548 (d) 554
Solution : As discussed above, we may label the given series as series I and then form series II to IV as shown below:
Series I : 3 20 63 144 275 ?
Series II: 17 43 81 131 ?
Series III: 26 38 50 ?
Series IV: 12 12
3, 7, 15, 31, ____ | |||
| Right Option : A | |||
| View Explanation | |||
17, 25, 41, 65, 97, ______________ | |||
| Right Option : C | |||
| View Explanation | |||
25, 20, 15, 10, _____ | |||
| Right Option : D | |||
| View Explanation | |||
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