Miscellaneous Series:
There are series that do not come
under the other patterns and are of general nature but are important and are
fairly common. Even here, sometimes, there can be a specific pattern in some
cases. .
Take the series 3, 5, 7, 11, 13, this
is a series of consecutive PRIME NUMBERS. It is an important series and the
student should look out for this as one of the patterns. The next term in this
series is 17.
There can also be variations using
prime numbers. Take the series 9, 25, 49, 121, In this series, the terms are
squares of prime numbers. Hence, the next term is 132, i.e., 169.
Take the series 15, 35, 77, .....The
first term is 3 x 5; the second term is 5 x 7; the third term is 7 x 11; here
the terms are product of two consecutive prime numbers. So, the next term will
be the product of 11 and 13, i.e., 143.
Take the series 8, 24, 48, 120, 168,
..... Here, the 2' term is 3 times the first term and the 3' term is 2 times
the 2nd term, but after that it does not follow this pattern any more. If you
look at the terms carefully, you will find that the terms are {one less than
squares of prime numbers}. Hence, the next term will be 172-1, i.e., 288.
Consider the series 1, 4, 9, 1, 6, 2,
5, 3, ... . . .
At first sight there is nothing we
can say about the series. This is actually a series formed by squares of
natural numbers. However, if any of t he squares is in two or more digits, each
of the digits is written as a separate term of the series. Thus, the first
terms are 1, 4 and 9, the squares of 1, 2 and 3 respectively. After this, we
should get 16 (which is the square of 4). Since this has two digits 1 and 6,
these two digits are written as two different terms 1 and 6 in the series.
Similarly, the next square 25 is written as two different terms 2 and 5 in the
series. So, the next square 36 should be written as two terms 3 and 6. Of
these, 3 is already given. So, the next term of the series is 6. Consider
the series 1, 1, 2, 3, 5, 8,………… .
1, 1, 2 , 3, 5 , 8
¯ ¯ ¯ ¯
1+1 1+2 2+3 3+5
Here, each term, starting with the third
number, is the sum of the two preceding terms. After taking the first two terms
as given (1 and 1), then onwards, to get any term, we need to add the two terms
that come immediately before that position. Hence, to get the next term of the
series, we should take the two Preceding terms 5 and 8 and add them up to get
13. So, the next term of the series is 13. The term after this will be 21 (= 8
+ 13).
