Corrected online exercises on number sequences.

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 11th Grade | 12th Grade
  • 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 11th Grade | 12th Grade
  • 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 11th Grade | 12th Grade
  • 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 11th Grade | 12th Grade
  • 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 11th Grade | 12th Grade
  • 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 11th Grade | 12th Grade
  • 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 11th Grade | 12th Grade
  • 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. .
    2. Compute `u_(5)`.
    "

    1627 numerical sequences 11th Grade | 12th Grade
  • 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 11th Grade | 12th Grade
  • 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 11th Grade | 12th Grade
  • 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 11th Grade | 12th Grade

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

List of exercises by class : middle and high schools, 6th Grade, 7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade, 12th Grade.

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