Pre Calculus >>> Arithmetic Sequence

HNO

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Hello there!

I am not able to show any work )= because I am unsure what a corresponding equation is. *** Here is the actual Question:

1. Given the arithmetic sequences 6, 10, 14, ...

a. Write the corresponding equation

b. Use your equation to find the y value when the x value is 17.

I'v bee taught the formula : Tn = T1 + (n -1) d and for many questions this is the main formula equation I use. I have not yet had a question with y and x mentioned and identifying the corresponding equation.

It would be great if you could help me out!! I apologize for not having some work for you to correct…. but I have no idea how to even start!
THANKS FOR YOUR HELP! :D
 
Last edited:
We've already seen one like this. Show us your result.

It si not good enough to show no work because you have none - for whatever reason. Stating a formula is SOME work.
 
Arithmetic

We've already seen one like this. Show us your result.

It si not good enough to show no work because you have none - for whatever reason. Stating a formula is SOME work.

****** Ok the only thing I can start off is by naming the terms and finding d

T1=6
T2=10
T3=14

d= 4

I dont understand what the corresponding equation is? Am I just writing the equation to find the next term?
 
****** Ok the only thing I can start off is by naming the terms and finding d

T1=6
T2=10
T3=14

d= 4
Okay. Now, you've been given a general formula (it's in your first post) and you've now found the values for T1 and for d. What is your specific formula, using the specific values of T1 and d, for this specific sequence? :wink:
 
Okay. Now, you've been given a general formula (it's in your first post) and you've now found the values for T1 and for d. What is your specific formula, using the specific values of T1 and d, for this specific sequence? :wink:


Well thats Tn= 6 + (n-1)4 >>>>> 4n-4 + 6 >>> 4n +2 = Tn
 
Well thats Tn= 6 + (n-1)4 >>>>> 4n-4 + 6 >>> 4n +2 = Tn

Now check to confirm:

. . . . .\(\displaystyle T_1\, =\, 6\, +\, (1\, -\, 1)4\, =\, 6\, +\, 0\, =\, 6\)

. . . . .\(\displaystyle T_2\, =\, 6\, +\, (2\, -\, 1)4\, =\, 6\, +\, 4\, =\, 10\)

. . . . .\(\displaystyle T_3\, =\, 6\, +\, (3\, -\, 1)4\, =\, 6\, +\, 8\, =\, 14\)

Do the results fit the original conditions? Then the formula must be valid, and your formula must be correct! :wink:
 
Now check to confirm:

. . . . .\(\displaystyle T_1\, =\, 6\, +\, (1\, -\, 1)4\, =\, 6\, +\, 0\, =\, 6\)

. . . . .\(\displaystyle T_2\, =\, 6\, +\, (2\, -\, 1)4\, =\, 6\, +\, 4\, =\, 10\)

. . . . .\(\displaystyle T_3\, =\, 6\, +\, (3\, -\, 1)4\, =\, 6\, +\, 8\, =\, 14\)

Do the results fit the original conditions? Then the formula must be valid, and your formula must be correct! :wink:

Thanks so much
 
Hello there!

I am not able to show any work )= because I am unsure what a corresponding equation is. *** Here is the actual Question:

1. Given the arithmetic sequences 6, 10, 14, ...

a. Write the corresponding equation

b. Use your equation to find the y value when the x value is 17.

I'v bee taught the formula : Tn = T1 + (n -1) d and for many questions this is the main formula equation I use. I have not yet had a question with y and x mentioned and identifying the corresponding equation.
Surely you understand that you can use whatever letters you want- that is, you can use "x" instead of "n" and "y" instead of "Tn"

It would be great if you could help me out!! I apologize for not having some work for you to correct…. but I have no idea how to even start!
THANKS FOR YOUR HELP! :D
Just putting the values you have given, T1= 6 and d= 4, you get Tn= 6+ 4(n-1)= 6+ 4n- 4= 4n+ 2, which, just changing variables, y= 6+ 4(x- 1)= 6+ 4x- 4= 4x+ 2. Having said that, if, as is the case in a usual "arthmetic sequence" (or any sequence), n must be an intger, then, as you have pointed out the first terms are 6, 6+ 4= 10, 10+ 4= 14, and then, 14+ 4= 18, having skipped over 17. But, if we allow x to be any number (which was probably the point of changing the variables), we can solve 6+ 4(x-1)= 17 for x. It will, of course, be between 3 and 4, closer to 4 than 3.
 
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