# recursive sequence calculator

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.
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)

### Recursive sequence, online calculus

#### 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.

#### 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;x) 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. .

#### 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)