Question

3. What is the 52nd term in the sequence?

9, 12.5, 16, 19.5, 23, . . .

Answer 1

you are adding the same number every time, correct? can you tell me what is it?

Answer 2

The constant number is 3.5 @SolomonZelman

Answer 3

yes, it is 3.5.

Answer 4

So you can state: \(\large\color{black}{ d=3.5 }\)

Now, you can see that \(\large\color{black}{ a_1}\) (the first term) is \(\large\color{black}{ 9 }\) .

Answer 5

a52 = 9 + 3.5(52), right?

Answer 6

Thank you very much. So now I just evaluate the equation and my answer will be given. I was just slightly confused on a1 and d in the equation.

Answer 7

oh you were a little off.

Answer 8

very smart, and what is \(\Large\color{black}{ a_{_{52}}=9+3.5(52-1) }\)

Answer 9

because the formula is: \(\Large\color{black}{ a_{_{52}}=a_1+9d(n-1) }\)

so you are plugging in accordingly: \(\Large\color{black}{ a_{_{52}}=9+3.5(52-1) }\)

Answer 10

formula should have just d, not 9d, sorry.

Answer 11

Can you explain briefly why the -1 is added? Is that like that in every ilteral term (or w/e its called) lol

Answer 12

By the way, my answer is 187.5

Answer 13

vconnection snapped before I could reply. Yes the answer is right...

Answer 14

It's okay, and thank you. :)

Answer 15

I'll explain this though, too.

You know that (in general) \(\large\color{black}{ a_2=a_1+d }\) , yes?

Answer 16

One last question, it's about common ratio's of a geometric sequence. And yes, I do.

Answer 17

Okay, so you wanted to explain why I subtract 1, inside the formula, right?
I can explain it like this:

you know that: \(\large\color{black}{ a_2=a_1+d }\)
\(\large\color{black}{ a_3=a_1+2d }\)
\(\large\color{black}{ a_4=a_1+3d }\)
\(\large\color{black}{ a_5=a_1+4d }\)

Answer 18

so this is where we get the formula, that: \(\large\color{black}{ a_n=a_1+4(n-1) }\)

right?

Answer 19

oooooohhhhh, ok, I get it now somewhat. thank you again for clearing it up for me!

Answer 20

I mean a formula that: \(\large\color{black}{ a_n=a_1+d(n-1) }\)

Answer 21

you are adding the difference one time less than the number of the term you want to find,

Answer 22

okay, and what would you like to know about geometric sequence?

Answer 23

Here's a picture of the question: http://i.gyazo.com/a82b7d26eee146ab9dccb416834d5c36.png

Answer 24

How about do you find the "common ratio" of a given geometric sequence, do you know?

Answer 25

okay, a common ratio is a number by which you multiply (each time) to obtain the next term in a sequence.

Answer 26

For instance, \(\large\color{black}{ a_{n-1} \times r=a_n }\) for any geometric sequence.

Answer 27

can you tell me what pattern do you notice in the terms (of your sequence) ?

Answer 28

From first glance, it looks hard. I can't really interpret the pattern.

Answer 29

I do see that it's getting smaller "...-3, -18...."

Answer 30

there is a formula: \(\large\color{black}{r=a_{n} \div a_{n-1} }\)
(where r is the common ratio)

basically divide any term by the term before, to find it:

For example:
\(\large\color{black}{r=a_{2} \div a_{1} }\)
Which in your case is:
\(\large\color{black}{r=(-\frac{1}{2}) \div (-\frac{1}{12}) }\)

Answer 31

I don't see the letters working, are they working for you?

Answer 32

Mhm, I see them working. Don't worry about it.

Answer 33

So I can divide any two terms to get the common ratio?

Answer 34

yes.

Answer 35

Do they have to be in a specific order or by each other? Say if I divided -1/12 by -18, there'd be no penalty/nothing wrong with that? Or should I divide -3 by -18 (vice versa).

Answer 36

no that would be wrong.

you are dividing a term, by another term that is (right) before.

Answer 37

Like:

\(\large\color{black}{r= (a_{3}) \div (a_2) }\)
\(\large\color{black}{r= (a_{4}) \div (a_3) }\)
or any,
\(\large\color{black}{r= (a_{n}) \div (a_{n-1}) }\)

but not: \(\large\color{black}{r= (a_{3}) \div (a_1) }\) (for example.)

Answer 38

Okay, so -18 by -3 would be the correct way of dividing & finding the common ratio of the sequence?

Answer 39

yes.

Answer 40

and what do you get the common ratio to be?

Answer 41

I seeeeee now, I see. Thank you again. I'll try dividing it right now, one second. I'll tag you when I'm finished.

Answer 42

and you can see how this actually works every time.

how:
~ (-1/12) * 6 = (-1/2)
~ (-1/2) * 6 = (-3)
~ (-3) * 6 = (-18)

and etc.

Answer 43

r=(-1/12*-18) divided by (-1/12*3-1) @SolomonZelman

Answer 44

I'm completely off lol. My answer was -5/4 (-1.25)

Answer 45

no no R can be equal to any of the following, because all have the same value:


r =
(-1/12) * 6 = (-1/2)

(-1/2) * 6 = (-3)

(-3) * 6 = (-18)

Answer 46

you see the 6 in there between any 2 terms?

Answer 47

(-1/12) * 6 = (-1/2)

(-1/2) * 6 = (-3)

(-3) * 6 = (-18)


means that r=6.

Answer 48

Oh, wow. I'm looking over it now. Thank you very much @SolomonZelman I'm pretty sure I can finish the rest of it on my own now, thanks to you lol. I gave you a medal & fanned you.

Answer 49

No need for a medal and fan, although you certainly can, if you want:)
you have been a joy to teach, no kidding. You grasped it quickly!

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