# Thread: A 16 team bowling league has $8,000 to be awarded as prize money. If the last place 1. ## A 16 team bowling league has$ 8,000 to be awarded as prize money. If the last place

A 16 team bowling league has $8,000 to be awarded as prize money. If the last place team is awarded$ 275 in prize money and the award increases by the same amount for
each successive finishing place, how much will the first place team receive?

a1 -- ? D = 275

an = a1=(n-1 ) d = 275
an = a1 + ( ( 16 - 1 ) d = 8000
a1(15)(275) = 8000
a14125 = 8000
a1 = 1.93

2. Originally Posted by r-soy
A 16 team bowling league has $8,000 to be awarded as prize money. If the last place team is awarded$ 275 in prize money and the award increases by the same amount for
each successive finishing place, how much will the first place team receive?

a1 -- ? D = 275

an = a1=(n-1 ) d = 275
an = a1 + ( ( 16 - 1 ) d = 8000
a1(15)(275) = 8000
a14125 = 8000
a1 = 1.93

I thought I had answered this before! First, you have "a1" and "d" swapped. "the last place team is awarded $275 in prize money" means that a1 is 275, not d. Second, you are asserting that the 16th position, the winning award, is 8000, not the sum. The nth value is, then, $a_n= 275+ (n-1)d$ and the sum, through n values is $\frac{n(550+ (n-1)d)}{2}$. Since the sum of all 16 prizes is to be 8000, you need to solve $\frac{16+ 15d}{2}= 8000$ for d and then find $a_{16}$. 3. Originally Posted by r-soy A 16 team bowling league has$ 8,000 to be awarded as prize money. If the last place
team is awarded \$ 275 in prize money and the award increases by the same amount for
each successive finishing place, how much will the first place team receive?

a1 -- ? D = 275

an = a1=(n-1 ) d = 275
an = a1 + ( ( 16 - 1 ) d = 8000
a1(15)(275) = 8000
a14125 = 8000
a1 = 1.93

This is an arithmetic sequence as you correctly pointed out.

We are given the total, the number and the first term.

$S_{16} = 8000$
$n = 16$
$a = 275$

$S_{16} = \frac{16}{2}(2 \cdot 275+15d) = 4400+30d = 8000$

Solve for the common difference $d$

Spoiler:
$d = 120$

Now you can work out what the highest person won using the value of d

$U_{16} = 275+15d$

Spoiler:
$\ 2075$

EDIT: bah, too slow