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Quantitative Aptitude > Progressions and Sequences
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Add Comment Bookmark share + Refresher MaterialFree Online Preparation for CAT 2009 with Minglebox e-CAT Prep. Cover basic concepts of Progressions, Sequences and Series under Quantitative Aptitude for MBA Entrance Exam Preparation with Study material, solved examples and tests prepared by CAT coaching experts.
A progression or sequence is defined as a succession of terms arranged in a definite according to some rule. For example the sequence of Odd numbers 1,3,5,7,9,11,etc......
The numbers in the sequence are called the terms of the sequence. A sequence having a finite number of terms is known as finite sequence. The first terms in a sequence is generally denoted by a,
the general term of the sequence, as by assigning value to 'n' ,
Example If the general term of a sequence is given by 2n, Find the First, sixth and 8 th term.
Given Tn = 2n Therefore First Term Therefore Similarly
Some Standard type of sequences:
Arithematic Progression (AP)
In this type of sequence, the difference between any two consecutive terms of the sequence is a constant. The constant is known as the 'Common difference.' Thus if the first term in AP is a, and Common difference is 'd' then second term is given by in general Sum of n terms of an AP is given by Also
Geometric Progression (GP)
In this type of sequence the ratio of 2 consecutive terms is a constant. The constant ratio is know as common ration and is usually denoted by 'r'. Thus if 'a' is the first terms of a GP then Sum of n terms of a GP, =
Sum up to infinite terms of a GP If higher values of n then large number of terms, we say the sum up to infinite terms,
Harmonic Progression (HP)
A sequence
if
The There is no formula for finding the sum up to n terms of a HP. Arithmetic mean (AM) of 2 positive numbers a,b is defined as Geometric mean (GM) of 2 positive numbers a,b is defined as Harmonic mean (HM) of 2 positive numbers a,b is defined as
Solved Examples Question Find the 10 th terms of the series: (1) (2) (3) (4)
Solution Term of the series can be split as We find 4,3,2....... are in AP with common difference of -1 hence 10 th term is given by [as Also Hence [as Hence
Question
If the 8 th term of an AP is 88 and the 88 th term is 8, then 100 th term is : (1) 1 (2) 2 (3) -4 (4) 8
Solution
Given 8 th = 88 and 88 th term = 8, let the first term of AP be 'a' and common difference be 'd'. then and 8 = a + 87d (2) Subtracting we get 80 = -80d and putting (1) we get a = 95 Hence, = 95 + 99(-1) = -4 Hence option (3)
Question
In the AP 3,7,11,15..... up to 50 terms and 2,5,8.....up to 50 terms, how many terms are identical ? (1) 12 (2) 4 (3) 16 (4) 18
Solution
For the AP 3,7,11,15....
and for the AP 2,5,8,.......
if 4n-1 = 3m-1 As Hence As x has to be an integer For x = 1,2,3......12 Thus there are 12 terms in the 2 sequences which are equal.
Question
The product of the first terms of the G.P having the third term as 24 as - (1) 16 (2) 32 (3) 64 (4) 128
Solution
Let the third term be 'a' then first, second fourth and fifth term will be given as Now product of first five terms = = but a = 2 Hence (2)
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second term by 
or
n=1
=2.1 = 2
= 2.6 = 12 and
= a+d, third terms 
= a+2d etc.....
= a+(n-1)d.
then 
------->0 as n-----> 
i.e. if lets say 
then if we consider higher and
becomes smaller and smaller. Hence if we consider the sum up to very
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