please help. A theater has 49 seats in the first row, 52 seats in the second row, 55 seats in the third row, and so on. Can the number of seats in each row be modeled by and arithmetic or geometric sequence? Write the general term for a_n that gives the number of seats in row n. How many seats are there in row 19?

Question

tyteen4a03 · Answer

Hint: The common difference can be found by subtracting $a_2$ to $a_1$.

tyteen4a03 · Answer

*subtracting $a_1$ from $a_2$, sorry

anonymous · Answer

so far i've got 49(n^(19-1)3

tyteen4a03 · Answer

What does n stand for?

anonymous · Answer

Thats where i'm lost. I'm trying to plug numbers into the formula.

tyteen4a03 · Answer

I think you need to rebuild the formula. The general term in here is a simple one - no need to raise powers and all that.

campbell_st · Answer

well start with the basics... the seating in modelled by an arithmetic sequence...and not a geometric sequence... 

the general term in an arithmetic sequence is 

$$a_{n} = a_{1} + (n -1) \times d$$

a1 is the 1st term, n = number of terms and d = common difference

anonymous · Answer

so n is 19.. so 49+(19-1)d. what is d supposed to be?

anonymous · Answer

3?

tyteen4a03 · Answer

@starlitxeyes Correct. You find d by subtracting a_1 from a_2.

campbell_st · Answer

thats correct... now you just need to distribute and collect like terms...

campbell_st · Answer

that gives the general equation, the 1st part... then substitute n = 19 for the 2nd part

anonymous · Answer

49+(19-1)3=103

anonymous · Answer

so row 19 has 103 seats

campbell_st · Answer

that is the 2nd part of the question... you still haven't got the general equation...

anonymous · Answer

an=49+(19-1)3

campbell_st · Answer

nope that is the answer to part b

$$a_{19} = 49 + (19 -1) \times 3$$

the general equation is 

$$a_{n} = 49 + (n -1) \times 3$$

simplify this equation for the general form.

anonymous · Answer

im so confused

campbell_st · Answer

ok... the question asks you to "... write the general form for a_n for the number of seats in row n..."

so 

$$a_{n} = 49 + ( n - 1)\times 3$$

distribute the 3

$$a_{n} = 49 + 3n - 3$$

now simplify the equation above for the general form... solution...

anonymous · Answer

46+3n   divide by 3... am I on the right track?

campbell_st · Answer

nope... thats it

$$a_{n} = 3n + 46$$

the general form

campbell_st · Answer

and if you substitute n = 19 you'll find you get 103

anonymous · Answer

oh! I over think things to often!

anonymous · Answer

Thanks!