Series / Sequences: Determine whether the number is an element 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?

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

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, $6$

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?

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, $7$

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, $9$

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, $8$

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?

Yes, $6$

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?

Yes, $5$

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?

No

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?

Yes, $10$

$a_n=n+5$

Is the number 15 a term in the sequence above?

Yes

A sequence has a term-to-term rule of $a_n= 15n$.

Is the number 30 a term in the sequence?

Yes, it is the second term.

$3n-3$

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?

Yes, it is the 14th term.

Is the shape ◯ in the sequence above?

Yes, in the fifth element