Determine whether if the sequence is arithmetic geometric or neither. Explain.

3, 3/2, 1, 3/4...

Skip to content# Determine whether if the sequence is arithmetic geometric or neither. Explain.3, 3/2, 1, 3/4…

##
This Post Has 11 Comments

### Leave a Reply

Determine whether if the sequence is arithmetic geometric or neither. Explain.

3, 3/2, 1, 3/4...

The following sequence shown up top is arithmetic sequence

x = 25

step-by-step explanation:

a^2+b^2=c^2

7^2+24^2=c^2

49+576=625

sqrt625=25

x=25

[tex]What is the value of x? enter your answer in the box. x =[/tex]

The sequence is given by the rule [tex]a_n=4n-2[/tex].

This means that the first, second and third terms of the sequence, [tex]a_1, a_2, a_3[/tex], are as follows:

[tex]a_1=4(1)-2=4-2=2[/tex]

[tex]a_2=4(2)-2=8-2=6[/tex].

[tex]a_3=4(3)-2=12-2=10[/tex].

Now, we can clearly see that 10-6=6-2 = 4. The sequence is arithmetic since the difference between two consecutive terms is the same.

We can also clearly see that the common difference is 4.

Remark: even without computing 2, 6, 10 above, we could see that each term contains one more 4 than the previous term. This is the only thing that changed, while 2 remained "intact".

Arithmetic; common difference d=4.

B

Step-by-step explanation:

A geometric sequence has a common ratio r between consecutive terms

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = ...

[tex]\frac{-14}{-7}[/tex] = 2

[tex]\frac{-28}{-14}[/tex] = 2

[tex]\frac{-56}{-28}[/tex] = 2

There is a common ratio of 2 between consecutive terms.

Hence sequence is geometric → B

The answer to number 2 is c

For number 1 the correct answer is D) -1

Number 3 is C) 0

Sorry that I don't know the others.

Hope this helps 🙂

all of them is geometric sequence

neither

Step-by-step explanation:

Consider sequence [tex]a_1 , a_2 , a_3 , .....a_n[/tex], where n acn be any natural number.

This sequence is said to be Arithmetic sequence if the difference between two consecutive terms is equal.

i.e, if it is arithmetic then [tex]d=a_2-a_1=a_3-a_2=...=a_n-a_{n-1}[/tex]

This sequence is said to be Geometric sequence if the common ratio between two consecutive terms is equal.

[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=......=\dfrac{a_n}{a_{n-1}}}[/tex]

The given sequence = 1, 2, 2, 3, ...

Here , [tex]2-1\neq2-2[/tex] , so difference between two consecutive terms is not equal.

⇒ Its not an Arithmetic sequence.

Also , [tex]\dfrac{2}{1}\neq\dfrac{2}{2}\neq\dfrac{3}{2}[/tex], so ratio between two consecutive terms is also not equal.

⇒ Its not an Geometric sequence.

Hence, the given sequence is neither arithmetic nor geometric.

Vhjjkkvvhjj

1.arithmetic , d= -1/5

2.geometric , r=4

3.arithmetic , d=9

4.arithmetic , d=4

Neither.for a sequence to be arithmetic, the difference between a term and the term before it has to be constant (common difference)2nd term minus 1st term4 - 1 = 33rd term minus 2nd term9 - 4 = 54th term minus 3rd term16 - 9 = 7the difference is not constant. not arithmetic.for a geometric seq, ratio of a term to the term before has to be common (common ratio)4 / 1 = 4 9/4 is not 4so not geometric.neither.