Series / Sequences: Complete the equation

The sequence below is structured according to a term-to-term rule.

What is the first element?

$\text{?}+\text{?}$

$2+4$

$3+7$

$4+10$

$5+13$

We start with the right column in the exercises.

Between each number there is a jump of +3:$4+3=7$

$7+3=10$

Etcetera.

Now we move to the left column of the exercises.

Between each number there is a jump of +1:

$2+1=3$

$3+1=4$

Now we can figure out which exercise is missing:

The left digit will be:$2-1=1$

The right digit will be:$4-3=1$

And the missing exercise is:$1+1$

$1+1$

Below is the rule for a sequence written in terms of $n$:

$2n+2$

Calculate the value of the 11th element.

We calculate by replacing$n=11$

$2\times11+2=$

First we solve the multiplication exercise and then we add 2:

$22+2=24$

$24$

Below is a sequence represented by squares. How many squares will there be in the 8th element?

It is apparent, that for each successive number, a square is added in length and one in width.

Hence, the rule using the variable n is:

$a(n)=n^2$

Therefore, the eighth term will be:

$n^2=8\times8=16$

$64$

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

A sequence has the following term-to-term rule:

$\frac{n}{2}$

What is the the third term?

The third term in the sequence is the term $a_3$meaning in the general term formula given:

$a_n= \frac{n}{2}$We need to substitute the position (of the requested term in the sequence):

$n=3$Let's do this:

$a_{\underline{n}}= \frac{\underline{n}}{2} \\ n=\underline{3}\\ \downarrow\\ a_{\underline{3}}=\frac{\underline{3}}{2}$When we substituted in place of n the position (of the requested term in the sequence): 3, the substitution is shown with an underline in the expression above,

Therefore, the correct answer is answer C.

$\frac{3}{2}$

Which shape appears in the fifth element of the sequence?

In a classroom there are 10 chairs numbered according to the constant property. Complete the series of chairs:

20 , 18

16 , 14

_ , _

8 , 6

4 , 2

12 , 10

Below is a sequence represented by squares. How many squares will there be in the 6th element?

36

Below is a sequence represented by squares. How many squares will there be in the 4th element?

$16$

Below is a sequence represented by squares. How many squares will there be in the 5 element?

$25$

Below is the rule for a sequence in terms of $n$:

$2(2n-2)$

What is the value of the 7th element in the sequence?

$24$

Below is the rule for a sequence written in terms of $n$:

$2(n+4)$

Work out the value of the 9th element in the sequence.

$26$

Below is a sequence of exercises.

The sequence adheres to a certain term-to-term rule.

Complete the missing element (?):

$6+5$

$5+4$

$\text{?}+\text{?}$

$3+2$

$2+1$

$4+3$

Below is a sequence represented with squares. How many squares will there be in the 7th element?

$49$

Which shape will appear in the fifth element of this sequence?

Choose which represents the fourth element of the sequence.

What is the shape of the fourth element?

$10n-9$

What are the fourth and fifth terms of the sequence above?

31, 41

A sequence represents the division of boys and girls into groups and is structured according to a term-to-term rule.

Complete group C.

13, 17

Below is a sequence of exercises.

The sequence adheres to a certain term-to-term rule. Complete the missing element (?):

$18+49$

$14+37$

$\text{?}+\text{?}$

$6+13$

$2+1$

$10+25$