sequences help

[yfelix45]

Hello,
I have been stuck on this question not really sure if I have done it right.

A theatre has eight (8) seats in the front seats. Each row has two (2) more seats than the row in front of it.

a) How many seats are in the 2nd, 3rd and 4th row. Write the first 4 terms in the sequence beginning with 8 in the first row.
ans:
1st..........8
2nd......... 10
3rd..........12
4th..........14

b) write a general t^n for this sequence

ans:
t^n = t^n + 2

c)Use the general term to determine how many seats are in the 20th row of the theatre.
ans: not sure if the answer from b) is right.

Am I on the right track? Can you guide me on the right way to solve this question?

Thanks

yfelix45

 

[biffboy]

This is an arithmetic sequence with 1st term 8 and common difference 2 so nth term is 8 +(n-1)*2=8+2n-2= 2n+6

 

[soroban]

Hello, yfelix45!

A theatre has eight (8) seats in the front seats.
Each row has two (2) more seats than the row in front of it.

a) How many seats are in the 2nd, 3rd and 4th row.
Write the first 4 terms in the sequence beginning with 8 in the first row.

answer
\(\displaystyle \begin{array}{cc}\text{1st} & 8 \\ \text{2nd} & 10 \\ \text{3rd} & 12 \\ \text{4th} & 14\end{array}\) . Correct!


b) Write the general term \(\displaystyle t_n\) for this sequence

ans:
t^n = t^n + 2 . no

You are writing a recursive relation.
Besides, it should be \(\displaystyle t_n \,=\,t_{n-1}+2\)

We want: .\(\displaystyle t_n \:=\:6+ 2n\)

(c) Use the general term to determine how many seats are in the 20th row of the theatre.

Plug \(\displaystyle n = 20\) into the above formula.

 

[yfelix45]

Thanks

Hello soroban and biffboy,

Thank you both for your help on this question. Your guidance is always appreciated.


Thanks

yfelix45

 

[HallsofIvy]

Hello,
I have been stuck on this question not really sure if I have done it right.

A theatre has eight (8) seats in the front seats. Each row has two (2) more seats than the row in front of it.

a) How many seats are in the 2nd, 3rd and 4th row. Write the first 4 terms in the sequence beginning with 8 in the first row.
ans:
1st..........8
2nd......... 10
3rd..........12
4th..........14

b) write a general t^n for this sequence

I take it you mean this as simply a superscript, not an exponent.

ans:
t^n = t^n + 2

You mean t^{n+1}= t^n+ 2- that the number of seats in each row is 2 more than in the previous row.

c)Use the general term to determine how many seats are in the 20th row of the theatre.
ans: not sure if the answer from b) is right.

What you give in (b) is NOT the "general term", it is just a restatement of the information. The "general term" would be something like
t^n= a formula involving n only. One way to do this is to recognize that since the condition is linear, the general term should be, at most, quadratic. Try something like t^n= An^2+ Bn+ C.
Now, determine A, B, and C to make this fit the information you have: when n= 1, t^1= A+ B+ C= 8. When n= 2, t^2= 4A+ 2B+ C= 10. When n= 3, t^3= 9A+ 3B+ C= 12. Those are three equations to solve for A, B, and C. Then you could use that fact that when n= 4, t^4= 16A+ 4B+ C= 14 as a check.

Am I on the right track? Can you guide me on the right way to solve this question?

Thanks

yfelix45