Question

Determine the second and third therms of an arithmetic sequence if: The First term is 42 and the fourth term is 27

Answer 1

an arithmetic sequence is one where successive terms differ by a fixed amount (the common difference). You have the first term = 42, and the fourth term = 27. You need to find the second and third terms.

42, x, y, 27

42-x = x-y = y-27

or

if a is the common difference,
42 - a = x
42 - 2a = y
42 - 3a = 27

you should be able to find a from the last equation, and then figure out the middle two terms.

Answer 2

I still don't get it.... like at all

Answer 3

i have to use the formula tn=t1+(n-1)d

Answer 4

okay, fine. Your formula is the equivalent of mine.

\[t_n = t_1+(n-1)d\]\(t_n\) is the \(n\)th term
\(t_1\) is the 1st term
\(n\) is the term you seek
\(d\) is the common difference (which you don't know yet)

We know \(t_1=42 \text{ and }t_4 = 27\)Can you fill those into the equation and tell me what you get after doing so?

Answer 5

use \(n=4\) because you are using \(t_4\)

Answer 6

ok--- \[42= 27+ (4-1)d\] Is that right?

Answer 7

Isn't the first term 42, and the 4th term 27?

Answer 8

you have them switched.

Answer 9

Oh woops sorry let me try again

Answer 10

\[27= 42+(4-1)d\]

Answer 11

Good, can you solve that for \(d\)?

Answer 12

so then d= 45?

Answer 13

show me your work that led to that answer

Answer 14

I just did 42+3 then that would equal 45 right?

Answer 15

what happened to \(d\)? and the 27 on the left?

Answer 16

I'm so confused

Answer 17

you have an equation:

\[27 = 42 + (4-1)d\]

Read in words, you could see that as "some number I don't know, which I'll call d, times the quantity 4-1, plus an additional 42, equals 27."

Answer 18

so 27= 45(d)

Answer 19

no! the right side of that equation is

\[42 + (4-1)*d\]

You can't just add 42 + (4-1) = 45!

Answer 20

What can we do with the \[(4-1)d\]?

We can distribute it:
\[(4-1)d = 4*d-1*d\]or we can simplify it:\[(4-1)d = (3)d = 3d\]
We could also distribute it, then simplify it:
\[(4-1)d=4*d-1*d=4d-d=3d\]

Answer 21

Welcome to OpenStudy @Animegurl3 !

Answer 22

OH!! I get it now... well the (4-1)d part so just simplifying makes the 3 the difference right?

Answer 23

uh, no. the value of \(d\) is the difference. We still need to find that.
\[27=42+(4-1)d\]we need to manipulate this equation so that we end up with just \(d\) on one side of the equals sign and a number on the other. You can add, subtract, multiply, divide, etc so long as you do the same thing to both sides of the equals sign.

Answer 24

oh okay so then 27=42+(4-1)d which becomes \[27=3d\] and then you divide 3 from both sided so then 9=d right?

Answer 25

Hey are you still there?

Answer 26

No, I'm banging my head on the desk :-)

\[27 = 42+(4-1)d\]How did you get from there to \[27=3d\]What happened to the \( 42\)?!?

Answer 27

Oh funny :). Sorry!

Umm... then 27=42+3d then subtract 42 from both sides and get -15=3d then divide 3 from both sides and -5=d HA That HAS to be right

Answer 28

yes, much better.

Now what happens if you add -5 to 42? What do you get? And if you add -5 to that number, what do you get? And if you add -5 to that number, what do you get? Discuss.

Answer 29

okay so then t1= 42 and t2=37 and t3=32 and t4=27

OMG I get Thank You soo MUCH

Answer 30

I GET IT I GET IT Thanx for having soo much patience with me :-) :-)

Answer 31

Dunno how he does it.

Answer 32

If only my teacher made this much sense. She basically mutters through the whole thing and gets angry when nobody gets it like in 3 seconds

Answer 33

it all balances out, I have 0 patience with the people who actually have to live with me :-)

Answer 34

haha :)

Answer 35

So, what is the 7th term of this sequence?