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?

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

$a_n=n+5$

Is the number 15 a term in the sequence above?

Yes

How many triangles are in the third element?

2

How many squares are there in the fourth element?

7

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.

A sequence has a rule of $n-4$.

Is the number 10 a term in the sequence?

Yes, it is the 14th term.

$3n-3$

Is the number 0 a term in the sequence above?

Yes, it's the first term.

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, $10$

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

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$n$:

$2n+2$

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$n$:

$4n-2$

Is the number 18 Is it part of the series? If so, what element is it in the series?

Yes, $5$

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

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

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, $7$

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, $6$

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, $8$

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, $9$

Assuming that the series continues with the same legality, does the number $-1$ Is it part of the series?

$51,47,43,39\ldots$

Yes