Determine whether the number 15 a term in the sequence above:
\( a_n=n+5 \)
Determine whether the number 15 a term in the sequence above:
According to the following rule\( a_n= 15n \).
Determine whether 30 is a term in the sequence:
Given a series whose first element is 15, each element of the series is less by 2 of its predecessor.
Is the number 1 an element of the series?
Look at the sequence below:
... ,1800, 1700, 1600, 1500
Which of the following numbers will appear in the sequence of numbers indicated above?
\( 3n-3 \)
Is the number 0 a term in the sequence above?
Determine whether the number 15 a term in the sequence above:
Determine whether the number 15 is a member of the sequence defined by the following expression:
This can be achieved in the following way:
Our first requirement is that the value 15 does in fact exist within the sequence regardless of its position.
Hence the following expression:
We will proceed to solve the equation obtained from this requirement. Remember that n is the position of the member in the sequence (also called - the index of the member in the sequence), and therefore must be a natural number ( a positive whole number).
Let's check whether these two requirements can be met:
First, let's solve:
We inserted into the first equation with its value from the second equation.
We obtained an equation with one unknown for n. Let's proceed to solve it by moving terms and isolating the unknown as shown below:
In the last step we divided both sides of the equation by the coefficient of the unknown on the left side,
Thus we met the requirement that:
Leading to:
This is indeed a natural number, - positive and whole. Therefore we can conclude that the number 15 is indeed present in the sequence defined in the problem, and its position is 10, meaning - in mathematical notation:
Therefore the correct answer is answer A.
Yes
According to the following rule.
Determine whether 30 is a term in the sequence:
Determine whether the number 30 is a term in the sequence defined by the given general term:
,
This can be achieved in the following way:
To begin with we require that such a term exists in the sequence, regardless of its position. Hence the expression below.
Next we will proceed to solve the equation obtained from this requirement. Remember that n is the position of the term in the sequence (also called - the index of the term in the sequence) N must therefore be a natural number,( a positive whole number).
Let's check if these two requirements can both be met:
First, let's solve:
When we substituted in the first equation with its value from the second equation,
we obtained an equation with one unknown for n. Let's solve it by moving terms and isolating the unknown as shown below:
In the last step we divided both sides of the equation by the coefficient of the unknown on the left side,
We thus met the requirement that:
Which is turn equals:
This is indeed a natural number - positive as well as whole. Therefore we can conclude that in the sequence defined in the problem by the given general term, the number 30 is indeed a term and its position is 2, meaning - in mathematical notation:
Therefore the correct answer is answer B.
Yes, it is the second term.
Given a series whose first element is 15, each element of the series is less by 2 of its predecessor.
Is the number 1 an element of the series?
We know that the first term of the series is 15.
From here we can easily write the entire series, until we see if we reach 1.
15, 13, 11, 9, 7, 5, 3, 1
The number 1 is indeed an element of the series!
Yes
Look at the sequence below:
... ,1800, 1700, 1600, 1500
Which of the following numbers will appear in the sequence of numbers indicated above?
2000
Is the number 0 a term in the sequence above?
Yes, it's the first term.
A sequence has a rule of \( n-4 \).
Is the number 10 a term in the sequence?
How many squares are there in the fourth element?
How many triangles are in the third element?
Given the series whose first element is 10.
Each term of the series is greater by 2.5 of its predecessor.
Is the number 22.5 an element in the series?
If so, please indicate your place in the series.
Given a series whose first element is 1.5.
Each element of the series is greater by 3 of its predecessor.
Is the number 29 an element in the series?
If so, please indicate your place in the series.
A sequence has a rule of .
Is the number 10 a term in the sequence?
Yes, it is the 14th term.
How many squares are there in the fourth element?
7
How many triangles are in the third element?
2
Given the series whose first element is 10.
Each term of the series is greater by 2.5 of its predecessor.
Is the number 22.5 an element in the series?
If so, please indicate your place in the series.
Yes,
Given a series whose first element is 1.5.
Each element of the series is greater by 3 of its predecessor.
Is the number 29 an element in the series?
If so, please indicate your place in the series.
No
The following is a series of structures formed by squares with side lengths of 1 cm.
Is it possible for a structure to have 46 squares? If so, which element of the series is it?
Here is a series of structures made of squares whose side length is 1 cm.
Is it possible to have a structure in the series that has 49 squares? If so, what element of the series is it?
The following is a series of structures formed by squares with side lengths of 1 cm.
Is it possible to have a structure in the series that has 81 squares? If so, what element of the series is it?
The following is a series of structures formed by squares with side lengths of 1 cm.
Is it possible to have a structure in the series that has 55 squares? If so, what element of the series is it?
The following is a series of structures formed by squares with side lengths of 1 cm.
Is it possible to have a structure in the series that has 64 squares? If so, what element of the series is it?
The following is a series of structures formed by squares with side lengths of 1 cm.
Is it possible for a structure to have 46 squares? If so, which element of the series is it?
No
Here is a series of structures made of squares whose side length is 1 cm.
Is it possible to have a structure in the series that has 49 squares? If so, what element of the series is it?
Yes,
The following is a series of structures formed by squares with side lengths of 1 cm.
Is it possible to have a structure in the series that has 81 squares? If so, what element of the series is it?
Yes,
The following is a series of structures formed by squares with side lengths of 1 cm.
Is it possible to have a structure in the series that has 55 squares? If so, what element of the series is it?
No
The following is a series of structures formed by squares with side lengths of 1 cm.
Is it possible to have a structure in the series that has 64 squares? If so, what element of the series is it?
Yes,
Given a formula with a constant property that depends on\( n \):
\( 2(2n-2) \)
Is the number 20 Is it part of the series? If so, what element is it in the series?
Given a formula with a constant property that depends on\( n \):
\( 4n-2 \)
Is the number 18 Is it part of the series? If so, what element is it in the series?
Given a formula with a constant property that depends on\( n \):
\( 2n+2 \)
Is the number 9 Is it part of the series? If so, what element is it in the series?
Given a formula with a constant property that depends on\( n \):
\( n-0.5n \)
Is the number 5 Is it part of the series? If so, what element is it in the series?
\( 2n^2 \)
Is the number 8 a term in the sequence above?
Given a formula with a constant property that depends on:
Is the number 20 Is it part of the series? If so, what element is it in the series?
Yes,
Given a formula with a constant property that depends on:
Is the number 18 Is it part of the series? If so, what element is it in the series?
Yes,
Given a formula with a constant property that depends on:
Is the number 9 Is it part of the series? If so, what element is it in the series?
No
Given a formula with a constant property that depends on:
Is the number 5 Is it part of the series? If so, what element is it in the series?
Yes,
Is the number 8 a term in the sequence above?
Yes.