# recursive sequence calculator

## Calculus recursive_sequence

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### Function : recursive_sequence

#### Summary :

The calculator of sequence makes it possible to calculate online the terms of the sequence, defined by recurrence and its first term, until the indicated index.

Recursive_sequence online

#### Description :

The calculator is able to calculate online the terms of a sequence defined by recurrence between two of the indices of this sequence.

It is also possible to calculate the elements of a numerical sequence when it is explicitly defined .

## Calculation of the terms of a sequence defined by recurrence

The calculator is able to calculate the terms of a sequence defined by recurrence between two indices of this sequence.

Thus, to obtain the elements of a sequence defined by u_(n+1)=5*u_n and u_0=2, between 1 and 4 , enter : recursive_sequence(5x;2;4;x) after calculation, the result is returned.

## Calculation of elements of an arithmetic sequence defined by recurrence

The calculator is able to calculate the terms of an arithmetic sequence between two indices of this sequence , from the first term of the sequence and a recurrence relation.

Thus, to obtain the terms of an arithmetic sequence defined by recurrence with the relation u_(n+1)=5*u_n et u_0=3, between 1 and 6 enter : recursive_sequence(5*x;3;6;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, from a relation of recurrence and the first term of the sequence.

Thus, to obtain the terms of a geometric sequence defined by u_(n+1)=3*u_n and u_0=2, between 1 and 4 , enter : recursive_sequence(3*x;1;4;x) 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. .

The calculator of sequence makes it possible to calculate online the terms of the sequence, defined by recurrence and its first term, until the indicated index.

#### Syntax :

recursive_sequence(expression;first_term;upper bound;variable)

#### Examples :

This example shows how to calculate the first terms of a geometric sequence defined by recurrence. u_(n+1)=4*u_n and u_0=-1 recursive_sequence(4*x;-1;3;x)

Calculate online with recursive_sequence (recursive sequence calculator)