# Sequences Calculator

Want to excel in sequences and solve all complex problems in no time? Here is the perfect guide to start learning sequence concepts efficiently and also assess your answers via free online calculators. If you are looking for reliable online tools that calculate the Number Sequence & display the output in seconds then here comes a list of sequences calculator - free online tools.

## Best Online Numbering Sequences Calculators List

A list of free online sequence calculators is here to assist in completing your homework and assignment tasks. The straightforward descriptions, accurate results with detailed steps will make you understand the concept so easily and quickly. After referring & trying out our sequences calculators, you won't leave us with sad faces as we promise you to provide solutions for given sequences in a fraction of seconds with steps.

### Arithmetic Sequence Calculator

By using this Arithmetic Sequence Calculator, you can easily calculate the terms of an arithmetic sequence between two indices of this sequence in a few clicks. The common form of an arithmetic sequence can be formulated as an = a1 + f × (n-1)

For Example, the sequence is 3, 5, 8, 11, 13, 15, 17……. The difference between the two successive terms is 2 therefore it is called the difference 'd'.

In the above example, we can see that a1= 3 and a2 = 5.

The difference between the two successive terms is

a2 – a1 = 2

a3 – a2 = 2

In an arithmetic sequence, if the first term is a1 and the common difference is d, then the nth term of the sequence is given by:

an= a1+ (n−1) d

= 3 + (7-1) x 2

= 3 + 12 = 15.

### Geometric Sequence Calculator

A geometric sequence is a sequence where every term bears a constant ratio to its preceding term. The formula for geometric sequence is an = arn - 1

Where 'an' is the nth term in the sequence, 'a' is the first term, 'r' is the common ratio between two numbers, and 'n' is the nth term to be obtained.

For Example, calculate the geometric sequence up to 6 terms if first term(a) = 8, and common ratio(r) = 3. The solution for this geometric sequence is explained below:

a = 8, d = 3

an = arn - 1

a1(first term) = 8 × 31 - 1= 8

a2(second term) = 8 × 32 - 1= 8 × 3 = 24

a3(third term) = 8 × 33 - 1= 8 × 9 = 72

a4(fourth term) = 8 × 34 - 1= 8 × 21 = 168

a5(fifth term) = 8 × 35 - 1= 8 × 24 = 192

a6(sixth term) = 8 × 36 - 1= 8 × 27 = 216

Hence, the geometric sequence is {8, 24, 72, 168, 192, 216).

### Harmonic Sequence Calculator

The online tool that helps kids in calculating the values of the harmonic numbers and their inverse is Harmonic Sequence Calculator. Make use of this nth harmonic number formula ie., H(N) = 1+1/2+1/3+...+1/N and solve the harmonic number sequence.

The nth term of the Harmonic Progression (H.P) = 1/ [a+(n-1)d]

### Sequence and Series Formulas

A list of a few fundamental formulas of arithmetic progression and geometric progression is given here in a tabular form. Have a look at the formulas of Sequence and Series below table and calculate the problems effortlessly:

 Arithmetic Progression Geometric Progression Sequence a, a+d, a+2d,……,a+(n-1)d,…. a, ar, ar2,….,ar(n-1),… Common Difference or Ratio Successive term – Preceding term   Common difference = d = a2 – a1 Successive term/Preceding term   Common ratio = r = ar(n-1)/ar(n-2) General Term (nth Term) an = a + (n-1)d an = ar(n-1) nth term from the last term an = l – (n-1)d an = 1/r(n-1) Sum of first n terms sn = n/2(2a + (n-1)d) sn = a(1 – rn)/(1 – r) if r < 1   sn = a(rn -1)/(r – 1) if r > 1

Where, a = first term, d = common difference, r = common ratio, n = position of term, l = last term

### Fibonacci Calculator

A set of numbers that each number in the sequence is a total of two numbers that instantly progress is called a Fibonacci sequence.

F0=0, F1=F2=1, and Fn=Fn−1+Fn−2

The Fibonacci formula is given as follows.

Fn = Fn−1 + Fn−2, where n > 1

For Example, the 10th term in the fibonacci sequence is 67 then find the next term of the sequence. We know that 11th term = 10th term × the golden ratio.

F11 = 67 × 1.618034

≈ 108.408.

### Sum of Linear Number Sequence Calculator

The Sum of Linear Number Sequence Calculator allowed kids & teachers to calculate the sum of the terms of a sequence between two indices of the series. Also, this online tool can be utilized in an appropriate approach to solve the partial sums of some series.

The formula to find the sum of linear number sequence is Initial Value = Final Value - (periods-1)*Difference or Sn = (n/2) *(a+l)

where:
n - nth value in sequence
a - initial value of sequence
d - difference in each value
l - last value in sequence

### What is Meant by the Sequence?

An ordered list of numbers is known as Sequence in maths. An Arithmetic sequence, Geometric Sequence, Harmonic Sequence, and Fibonacci series are the four types of sequence. In the sequence, each number is recognized as a term. The three dots at the edge of the sequence indicates that the pattern of numbers will be continued.

Example:Let us consider 2, 4, 6, 8, 10,... as a sequence. From this example, you can find the first term of the sequence is 2, the second term is 4, and so on. The difference between each term is 2 and hence the common difference is 2 so that the continued sequence can be calculated by adding 2 to the previous term.

### What are Types of Sequence and Series?

Sequences: A finite sequence ends at the edge of the list of numbers like a1, a2, a3, a4, a5, a6……an. whereas, an infinite sequence is never-ending i.e. a1, a2, a3, a4, a5, a6……an…..

Series: In a finite series, a finite number of terms are written like a1 + a2 + a3 + a4 + a5 + a6 + ……an. In the case of an infinite series, the number of elements is not finite i.e. a1 + a2 + a3 + a4 + a5 + a6 + ……an +…..

### What are the first values of the Harmonic Series?

A list of first harmonic numbers are given here in a table:

n H(n) ≈H(n)
1 1/1 1
2 3/2 1.5
3 11/6 1.83333
4 25/12 2.08333
5 137/60 2.28333
6 49/20 2.45
7 363/140 2.59286
8 761/280 2.71786
9 7129/2520 2.82896
10   2.92897
100   5.18738
1000   7.48547
10000   9.78761
100000   12.09015
1000000   14.39272
10000000   16.69531
100000000   18.99790
1000000000   21.30048

### FAQs on Calculating Sequences Tools

1. What is the function of the sequence calculator?

The sequence calculator's main function is to calculate the sequence of the given function. SequenceCalculatorâ€™s online sequence calculators solve the given input instantly and provide the final sequence of the function within no time.

2. How do you find the next terms of a sequence?

Subtract the first term from the second term and the second term from the third term to find out the common difference for the sequence. To find the next term for the sequence, add the common difference to the last given term.

3. What kind of sequence is 2 4 8?

The given kind of sequence 2 4 8 is a Geometric sequence.

4. What kind of sequence is 2 5 8?

The sequence of 2 5 8 is an arithmetic sequence because there is a common difference between each term.

5. Where can I find the Arithmetic Sequence Calculator?

SequenceCalculators.com is a trusted and reliable website that provides free online calculator tools for all sequence concepts such as Arithmetic Sequence Calculator, Geometric Sequence Calculator, Sequence and Series Formulas, Fibonacci Calculator, Sum of linear number sequence Calculator, and Harmonic Sequence Calculator.