Question

Determine whether each sequence is arithmetic. if so, identify the common difference and find the 32nd term.

Sequence: 2, 5, 9, 14

I know how to do it when the increase is constant but I don't know how to change it when it goes up by different numbers. @kc_kennylau

Answer 1

First of all is it arithmetic?

Answer 2

Yes?

Answer 3

Or is that only when it goes up by a constant number?

Answer 4

It's no.. Ha sorry

Answer 5

You're correct, that's a no :)

Answer 6

Okay, so different question. When trying to find the missing term and theres more than one, how would the equation change from just have 2 on the bottom?

Answer 7

Uh... Sorry I don't get what you mean :/

Answer 8

I have to find the missing term in the sequence 2, ___, ___, ___, -0.4
I did another one like that one^^ but I only had to find one term and the equation was simply 11+27/2
I thought that the dominator corresponded with whatever term you had to find but my idea on that didn't work. How do I find the the answer for this one?

Answer 9

If you have the first term and the common difference you can generate the whole sequence right?

Answer 10

I'll denote the first term be "a" and the common difference be "d" from now on

Answer 11

If you have "a" and "d", the whole sequence is:
a, a+d, a+2d, a+3d, ..., a+(n-1)d

Answer 12

Um, I don't know. My book looks different..

Answer 13

What does your book say

Answer 14

The difference is 0.8 :>

Answer 15

Nope it isn't

Answer 16

Yes, it is.

2-0.8 = 1.2

1.2 - 0.8 = 0.4

0.4 - 0.8 = -0.4

Answer 17

Okay, so my the original problem says: Find the missing term(s) of each arithmetic sequence.

Sequence: 2, ___, ___, ___, -0.4

Answer 18

And no it isn't @tHe_FiZiCx99

Answer 19

So let a be the first term and d be the common difference, n=5 as there are 5 terms

Answer 20

a=2
a+(5-1)d=-0.4

Answer 21

Let's solve for d

Answer 22

Can you please write there equation in the equation maker thing so I can see it? It makes it easier for me..

Answer 23

What difference does it make?
\[a=2\]\[a+(5-1)d=-0.4\]

Answer 24

I don't know, it's just easier for me to see it clearly. I'm a better visual learner..

Answer 25

So solve for d?

Answer 26

Okay, one second.

Answer 27

It's -0.8 ._.

Yes, you have a 3 number space gap so subtract 2 - (-0.4) = 2.4 / 3 = 0.8

a_n = a1 + d(n-1)
a_2 = 2 + (-0.8)(2-1)
a_2 = 2 + (-0.8)(1)
a_2 = 2 - 0.8
a_2 = 1.2


Alternatively you can skip the last digit (4)

a_5 = 2 + (-0.8)(4-1)
a_5 = 2 + (-0.8)(3)
a_5 = 2 + (-2.4)
a_5 = -0.4

Answer 28

d= -0.4 ?

Answer 29

Nope :/

Answer 30

That 5 is a typo X_X

Answer 31

No to me or to him?

Answer 32

@tHe_FiZiCx99 double check it
@Nicole143 to you

Answer 33

Okay, um. I don't know then.

Answer 34

How did you solve it? Maybe I can find what's wrong in your steps

Answer 35

I may have done it wrong from the beginning.

2 + (5+1)d = -0.4
-2
6d = -2.4 / 6
d = -0.4

Answer 36

Oh, 0.8 skips one dash. Yeah, typo. >.<

Answer 37

It's 5-1 instead of 5+1

Answer 38

to Nicole

Answer 39

Oh, okay. One second.

Answer 40

D = -0.6

Answer 41

Yep :)

Answer 42

So can you find now the second term, the third term and fourth term?

Answer 43

Hint: The first term is a, the second term is a+d, the third term is a+2d, ...

Answer 44

Use 3 and 4 instead of 2?

Answer 45

Nope

Answer 46

You now have a=2 and d=-0.6

Answer 47

Find the second term i.e. a+d

Answer 48

What?

Answer 49

Find a+d

Answer 50

-2.6 ??

Answer 51

What's 2+(-0.6)

Answer 52

1.4 ...

Answer 53

Exactly

Answer 54

So do I then replace 2 for 3 and 4? Then take a+d form those equations for the next two?

Answer 55

You don't replace 2

Answer 56

2 is the first term

Answer 57

What do I replace to get the next 2 term?

Answer 58

The first term is the first term;
The second term is the first term plus the common difference;
The third term is the first term plus twice the common difference;
The fourth term is the first term plus thrice the common difference;
The fifth term is the first term plus four times the common difference.

Answer 59

\(a_1=a\)
\(a_2=a+d\)
\(a_3=a+2d\)
\(a_4=a+3d\)
\(a_5=a+4d\)

Answer 60

The common difference being -0.6 ?

Answer 61

Yes

Answer 62

Okay, so the third term would be .8 and the fourth would be .2 ?

Answer 63

Exactly

Answer 64

Great! Thank you!

Answer 65

Any questions? Asking questions is an effective way of learning

Answer 66

I don't think so

Answer 67

>.> I see why I got 0.8, missed adding a 1 to the divisor :/

Answer 68

@tHe_FiZiCx99 Glad you know where your mistake is.

Answer 69

@Nicole143 okay :)

Answer 70

Ahem, was* xD and it's a shortcut to getting the difference lol

Answer 71

Lol my grammar sucks xp

Answer 72

And you're right it's a shortcut but still derived from my way

Answer 73

a=2 and a+(5-1)d=-0.4

Answer 74

(2)-(1): (5-1)d=-0.4-2

Answer 75

d=(-0.4-2)/(5-1)

Answer 76

which is your way

Answer 77

Mine was actually dividing lol

2 + 0.4= 2.4/4 = 0.6

because it's decreasing you add the negative sign.

Answer 78

Yep that's just the same :)

Answer 79

Simpler lol

Answer 80

Can you help me with another?

Answer 81

I just tried to do it the same way we did another before but it didn't work..

Answer 82

I don't have time, so @tHe_FiZiCx99 will help you I suppose?

Answer 83

Okay, @tHe_FiZiCx99 can you help?

Answer 84

Um sure

Answer 85

Okay, the problem is finding the explicit formula for the arithmetic sequence.

Sequence: 62, 59, 56, 53

I tried doing the same thing that kc showed me before but it didn't come out with the right answer..

Answer 86

What was your answer?

Answer 87

an = 3n + 65

Answer 88

The common difference is -3 instead of 3 :)

Answer 89

Common difference = Second-first = Third-second = Fourth-third = ...

Answer 90

Yes, I did that part

Answer 91

It should be -3n instead of 3n

Answer 92

But the book says that the answer should be an=62-3(n-1)

How do I get that?

Answer 93

Oh, I just helped you expand it

Answer 94

Maybe my way wasn't the standard way :P

Answer 95

So what's the common difference

Answer 96

Haha okay, so dod you know how to get to that answer?

Answer 97

*do