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.
Find the 50th term of the sequence 2, 5, 8, 11 …
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,
This is how arithmetic sequence works.
Find the 10th term of the sequence 1, 2, 4, 8……
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
Now the 10th term of the geometric sequence will be calculated by using the above formula
GS=a*rn-1 = 1*(2)10-1
This is how we proceed with geometric sequence.