Corrected online exercises on number sequences.

Exercise example N°1614 :

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)`

numerical sequences 11th Grade sequence

The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined from a rational fraction function.

Exercise example N°1615 :

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)`

numerical sequences 11th Grade sequence

The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by a linear function.

Exercise example N°1616 :

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)`

numerical sequences 11th Grade sequence

The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by a power function.

Exercise example N°1617 :

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)`

numerical sequences 11th Grade sequence

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 N°1618 :

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)`

numerical sequences 11th Grade recursive_sequence

The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by recurrence with a linear function.

Exercise example N°1619 :

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)`

numerical sequences 11th Grade recursive_sequence

The purpose of this exercise on numerical sequences is to calculate terms of a sequence defined by recurrence with a quadratic function.

Exercise example N°1620 :

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)`.

numerical sequences 11th Grade 12th Grade

The purpose of this exercise on numerical sequences is to write in algebraic form one of the terms of the sequence.

Exercise example N°1621 :

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

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

numerical sequences 11th Grade 12th Grade

The purpose of this exercise on numerical sequences is to write in algebraic form one of the terms of the sequence.

Exercise example N°1622 :

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?

numerical sequences 11th Grade 12th Grade

Exercise on the direction of variation of a simple numerical sequence: constant sequences, increasing sequences and decreasing sequences.

Exercise example N°1623 :

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?

numerical sequences 11th Grade 12th Grade

Exercise on the direction of variation of a numerical sequence with a fraction: constant, increasing and decreasing sequences.

Exercise example N°1624 :

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.

numerical sequences 11th Grade 12th Grade

Exercise on arithmetic sequences, on geometric sequences and on common difference and on common ratio.

Exercise example N°1625 :

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.

numerical sequences 11th Grade 12th Grade

Exercise on geometric sequences, on arithmetic sequences and their reason.

Exercise example N°1626 :

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)`

numerical sequences 11th Grade 12th Grade

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 N°1627 :

"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. Compute `u_(5)`.

numerical sequences 11th Grade 12th Grade

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 N°1628 :

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.

numerical sequences 11th Grade 12th Grade

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 N°1629 :

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

numerical sequences 11th Grade 12th Grade

This exercise allows you to practice calculating the sum of the terms of an arithmetic sequence.

Exercise example N°1630 :

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.

numerical sequences 11th Grade 12th Grade

This exercise allows you to practice calculating the sum of the terms of a geometric sequence from its common ratio and its first term.