Sequence Calculator

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A set of numbers occurring in a definite order or by a rule is called a sequence. Thus any set of numbers a1, a2......an..., such that to each positive integer n, there corresponds a number an is sequence.   Sequences of special types are called progressions.
 
The sequence calculator is used to calculate Arithmetic sequence and Geometric sequence.
 
A sequence a1 a2 a3 is said to be in Arithmetic sequence when        a2-a1=a3-a2=........=an-an-1.
 
In this case, common difference is generally denoted by‘d’ and first term is denoted by a.
 
A sequence a1 a2 a3 is said to be in Geometric sequence when  
a2/ a1 = a3/ a2 = ...... = an/ an-1.
  
In this case, common ratio is generally denoted by ‘r’ and first term is denoted by a.



Example 1.
 
Find the 50th term of the sequence 2, 5, 8, 11 …
 
Solution:
 
The sequence 2, 5,8,11...... is an arithmetic sequence having common difference d = 3.
 
We know that, the nth term in arithmetic sequence is a1+ (n-1)*d
 
Common difference, d = 5-2=8-5=11-8=.....= 3
 
Here a = first term=2, d=3   and n=50
 
We know that the nth term of Arithmetic sequence equals to a+ (n-1)*d
 
Then we put the respective values for each term and we get as,
 
                                                 2+ (50-1)*3=2+49*3=149
 
This is how arithmetic sequence works.



Example 2.
 
 Find the 10th term of the sequence 1, 2, 4, 8……
 
Solution:
 
The sequence 1, 2, 4, 8…… is a geometric sequence with common ratio as 2.
 
We know that, nth term in geometric sequence is arn-1
 
Here,
 
a=first term=1,  
 
r=common ratio=2,
 
And n=10.
 
Now the 10th term of the geometric sequence will be calculated by using the above formula
 
GS=a*rn-1        = 1*(2)10-1
                               = 29.
                               = 24*25
=512.
                  
 
This is how we proceed with geometric sequence.


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