This online calculator can solve arithmetic sequences problems. Currently, it can help you with the two common types of problems:
Find the n-th term of an arithmetic sequence given m-th term and the common difference. Example problem: An arithmetic sequence has a common difference equal to 10, and its 5-th term is equal to 52. Find its 15-th term.
- Find the n-th term of an arithmetic sequence given i-th term and j-th term. Example problem: An arithmetic sequence has its 5-th term equal to 12 and its 15-th term equal to 52. Find its 20-th term.
Some formulas and descriptions of the solutions can be found below the calculator.
Arithmetic sequence calculator and problems solver
Problem type
Find term by another term and common difference
Find term by two another terms
First Term of the Arithmetic Sequence
nth Term of the Sequence Formula
Arithmetic sequence
To recall, an arithmetic sequence or arithmetic progression (AP) is a sequence of numbers such that the difference, named common difference, of two successive members of the sequence, is a constant.
Thus, the formula for the n-th term is
and in general
,
where d is the common difference.
You can solve the first type of problems listed above by using the general formula directly or calculating the first term a1, using the formula.
And then using the formula for the n-th term.
For the second type of problem, you need to find common difference using the following formula derived from the general formula.
After that, it becomes the first type of problem.
The calculator above also calculates the first term and general formula for the n-th term of an arithmetic sequence for convenience.
Summary :
Sequence calculator allows to calculate online the terms of the sequence whose index is between two limits.
sequence online
Description :
The sequence calculator is able to calculate online the terms of a sequence between two of the indices of this sequence.
Calculating the terms of a suite
The calculator is able to calculate the terms of a sequence between two indices of this sequence.
Thus, to obtain the elements of a sequence defined by `u_n=n^2` between 1 and 4 , it is necessary to enter : sequence(`n^2;1;4;n`) after calculation, the result is returned `u_1=1 ; u_2=4 ; u_3=9 ; u_4=16`.
The sequences can also be calculated by recurrence, for that, it is necessary to use the the calculator of sequences defined by recurrence .
Calculation of elements of an arithmetic sequence
The calculator allows to calculate the terms of an arithmetic sequence between two indices of this sequence
Thus, to obtain the terms of an arithmetic sequence defined by `u_n=3+5*n` between 1 and 4 , enter : sequence(`3+5*n;1;4;n`) after calculation, the result is returned.
Calculation of the terms of a geometric sequence
The calculator is able to calculate the terms of a geometric sequence between two indices of this sequence.
Thus, to obtain the terms of a geometric sequence defined by `u_n=3*2^n` between 1 and 4 , enter : sequence(`3*2^n;1;4;n`) after calculation, the result is returned.
Calculation of the sum of the terms of a sequence
The calculator is able to calculate the sum of the terms of a sequence between two indices of this series, it can be used in particular to calculate the partial sums of some series. .
Syntax :
sequence(sequence;lower bound;upper bound;variable)
Examples :
sequence(`n^2;1;4;n`), returns `u_1=1 ; u_2=4 ; u_3=9 ; u_4=16`.
Calculate online with sequence (sequence calculator)
The following arithmetic sequence calculator will help you determine the nth term and the sum of the first n terms of an arithmetic sequence.
Guidelines to use the calculator
If you select an, n is the nth term of the sequence
If you select Sn, n is the first n term of the sequence
For more information on how to find the common difference or sum, see this lesson arithmetic sequence
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