Here is the list of exercises on numerical sequences. Each corrected exercise is accompanied by indications, reminders of the course, and methodological advice, which allows you to practice independently.

17 exercises
• N°1614 (numerical sequences) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined from a rational fraction function.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(n)=(-5-4*n)/(4+3*n).
1. Compute u_(0)
2. Compute u_(1)

1614 numerical sequences 11th Grade sequence
• N°1615 (numerical sequences) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by a linear function.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(n)=-4-4*n.
1. Compute u_(3)
2. Compute u_(7)

1615 numerical sequences 11th Grade sequence
• N°1616 (numerical sequences) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by a power function.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(n)=(-1)^n*4^(n+1).
1. Compute u_(1)
2. Compute u_(2)

1616 numerical sequences 11th Grade sequence
• N°1617 (numerical sequences) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined from a fraction and a square root.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(n)=sqrt(3+3*n)/(5+3*n).
1. Compute u_(4)
2. Compute u_(6)

1617 numerical sequences 11th Grade sequence
• N°1618 (numerical sequences) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by recurrence with a linear function.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(0)= 2  and u_(n+1) = 1+u_(n).
1. Compute u_(3)
2. Compute u_(5)

1618 numerical sequences 11th Grade recursive_sequence
• N°1619 (numerical sequences) : The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by recurrence with a quadratic function.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(0)= 2  and u_(n+1) = -2+2*u_(n)^2.
1. Compute u_(2)
2. Compute u_(4)

1619 numerical sequences 11th Grade recursive_sequence
• N°1620 (numerical sequences) : The purpose of this exercise on numerical sequences is to write in algebraic form one of the terms of the sequence.

Exercise example :

Let the sequence (u_(n)) defined by u_(n) = (2+n)/(2+5*n).

Express as a function of n the terms of u_(n+3).

1620 numerical sequences
• N°1621 (numerical sequences) : The purpose of this exercise on numerical sequences is to write in algebraic form one of the terms of the sequence.

Exercise example :

Let the sequence (u_(n)) defined by u_(n) = -3-3*n.

Express as a function of n the terms of u_(n+1).

1621 numerical sequences
• N°1622 (numerical sequences) : Exercise on the direction of variation of a simple numerical sequence: constant sequences, increasing sequences and decreasing sequences.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(0)= 3  and u_(n+1) = -3+u_(n).
Is this sequence increasing or decreasing?

1622 numerical sequences
• N°1623 (numerical sequences) : Exercise on the direction of variation of a numerical sequence with a fraction: constant, increasing and decreasing sequences.

Exercise example :

Let the sequence (u_(n)) be defined for any natural number n by u_(0)= 4  and u_(n+1) = u_(n)/5.
Is this sequence increasing or decreasing?

1623 numerical sequences
• N°1624 (numerical sequences) : Exercise on arithmetic sequences, on geometric sequences and on common difference and on common ratio.

Exercise example :

Let the sequence (u_(n)) defined for any natural number n by u_(0)= -3  and u_(n+1) = -7+u_(n).

1. Is (u_(n)) an arithmetic or a geometric sequence ?
2. What is the reason of (u_(n))
3. Give the expression of u_(n) as a function of n.

1624 numerical sequences
• N°1625 (numerical sequences) : Exercise on geometric sequences, on arithmetic sequences and their reason.

Exercise example :

Let the sequence (u_(n)) defined for any natural number n by u_(0)= -1  and u_(n+1) = -9*u_(n).

1. Is (u_(n)) an arithmetic or a geometric sequence?
2. What is the reason of (u_(n)).
3. Give the expression of u_(n) as a function of n.

1625 numerical sequences
• N°1626 (numerical sequences) : This exercise allows you to practice the calculation of the terms of an arithmetic sequence from its common difference and its first term.

Exercise example :

Let (u_(n)) be an arithmetic sequence of common difference -6, and of first term u_(0)= 1 .

1. Give the expression of u_(n) as a function of n.
2. Compute u_(3)

1626 numerical sequences
• N°1627 (numerical sequences) : This exercise allows you to practice the calculation of the terms of a geometric sequence from its common ratio and its first term.

Exercise example :

"Let (u_(n)) be a geometric sequence of reason 8, and of first term u_(0)= 2 .
1. Give the expression of u_(n) as a function of n
2. .
3. Compute u_(5).
"

1627 numerical sequences
• N°1628 (numerical sequences) : This exercise allows you to practice calculating the sum of the terms of an arithmetic sequence from its common difference and its first term.

Exercise example :

Let (u_(n)) be an arithmetic sequence of common difference 6, and of first term u_(0)= 1. Let S be the sum of u_(3) to u_(25). S=u_(3)+u_(4)+u_(5)+. . .+u_(25).
1. Compute the number of terms in S.
2. Compute S.

1628 numerical sequences
• N°1629 (numerical sequences) : This exercise allows you to practice calculating the sum of the terms of an arithmetic sequence.

Exercise example :

Let S be the sum defined by S = 1.
1. Compute the number of terms in S.
2. Compute S.

1629 numerical sequences
• N°1630 (numerical sequences) : This exercise allows you to practice calculating the sum of the terms of a geometric sequence from its common ratio and its first term.

Exercise example :

Let (u_(n)) be a geometric sequence of common ratio -2, and of first term u_(0)= -2 . Let S be the sum of u_(2) to u_(14). S=u_(2)+u_(3)+u_(4)+. . .+u_(14).
1. Calculate u_(2)
2. Calculate u_(14).
3. Deduce S.

1630 numerical sequences

The numerical sequences topic is available for : 11th Grade, 12th Grade