1. ## Arithmetic sequence

Vivienne starts counting going by 3s from 4:
4,7,10,13….
Chloe starts counting backwards from 744 by 7s:
744, 737, 730, 723
They start saying their sequences at the same time and simultaneously say one number every second
i)What is the difference between the 7th numbers they both say?
(Using the arithmetic sequence formula) – I got 682 which is not the right answer ><
ii)Which number do they both say at the same time?
I need some help with this question, thank you for any help given

2. Originally Posted by christina
Vivienne starts counting going by 3s from 4:
4,7,10,13….
Chloe starts
counting backwards from 744 by 7s:
744, 737, 730, 723
They start saying their sequences at the same time and simultaneously say one number every second
i)What is the difference between the 7th numbers they both say?
(Using the arithmetic sequence formula) – I got 682 which is not the right answer ><
ii)Which number do they both say at the same time?
I need some help with this question, thank you for any help given
Use the formula for the nth term of an arithmetic sequence $\displaystyle U_n = a+(n-1)d$. For example

$\displaystyle U_7 = a+6d$

Spoiler:
Chloe: $\displaystyle U_7 = 744-42 = 702$
Viv : $\displaystyle U_7 = 4 + 18 = 22$

Difference is $\displaystyle 702-28 = 674$

ii) $\displaystyle U_n = 4+3n-3 = 3n+1$

$\displaystyle U_n = 744-7n+7 = 751-7n$

They will be equal and solve for $\displaystyle n=75$

3. Originally Posted by christina
Vivienne starts counting going by 3s from 4:
4,7,10,13….
Chloe starts counting backwards from 744 by 7s:
744, 737, 730, 723
They start saying their sequences at the same time and simultaneously say one number every second
i)What is the difference between the 7th numbers they both say?
(Using the arithmetic sequence formula) – I got 682 which is not the right answer ><
ii)Which number do they both say at the same time?
I need some help with this question, thank you for any help given
First sequence:

$\displaystyle t_n = 4 + 3(n - 1)$

so $\displaystyle t_7 = 4 + 3(7 - 1)$

$\displaystyle = 22$.

Second sequence:

$\displaystyle t_n = 744 - 7(n - 1)$

so $\displaystyle t_7 = 744 - 7(7 - 1)$

$\displaystyle = 702$.

So the difference between them is $\displaystyle 702 - 22 = 680$.

4. Originally Posted by e^(i*pi)
Use the formula for the nth term of an arithmetic sequence $\displaystyle U_n = a+(n-1)d$. For example

$\displaystyle U_7 = a+6d$

Spoiler:
Chloe: $\displaystyle U_7 = 744-42 = 702$
Viv : $\displaystyle U_7 = 4 + 24 = 28$

Difference is $\displaystyle 702-28 = 674$

ii) $\displaystyle U_n = 4+3n-3 = 3n+1$

$\displaystyle U_n = 744-7n+7 = 751-7n$

They will be equal and solve for $\displaystyle n=75$
Actually Viv's is

$\displaystyle U_n = 4 + 3(n - 1)$

$\displaystyle U_7 = 4 + 3(7 - 1)$

$\displaystyle = 22$.

5. Originally Posted by Prove It
Actually Viv's is

$\displaystyle U_n = 4 + 3(n - 1)$

$\displaystyle U_7 = 4 + 3(7 - 1)$

$\displaystyle = 22$.
Yeah it is, for some reason I put the common difference as 4

6. Originally Posted by christina
Vivienne starts counting going by 3s from 4:
4,7,10,13….
Chloe starts counting backwards from 744 by 7s:
744, 737, 730, 723
They start saying their sequences at the same time and simultaneously say one number every second
i)What is the difference between the 7th numbers they both say?
(Using the arithmetic sequence formula) – I got 682 which is not the right answer ><
ii)Which number do they both say at the same time?
I need some help with this question, thank you for any help given
Since they are saying the numbers at intervals of one second, they will say $\displaystyle a_n$ and $\displaystyle b_n$ at second "n". The first sequence, as other have told you is $\displaystyle a_n= 4+ 3(n-1)$ and the other is $\displaystyle b_n= 774- 5(n-1)$.

To find the number they say both say at the same time, solve $\displaystyle a_n= 4+ 3(n-1)= 774- 5(n-1)= b_n$ for n, then put it into either of the formulas to find the number.

7. thank you so much for all your help guys ! i really appreciate it ^^