Prize Money for 1st Place in 16 Team Bowling League: $1,930

[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?

My answer :

a1 -- ? D = 275

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

 

[HallsofIvy]

Does that even make sense to you? You are saying that if the last place team won $275, the first place team must have won $ 1.93!

You are told that a_1= 275- "If the last place team is awarded $ 275 in prize money" so 275 is the smallest amount in this arithmetic sequence, not the common difference.

If an arithmetic sequence has initial amount a_1 and common difference d, then the nth number is a_1+ (n-1)d and the sum is (a_1+ (n-1)d/2)n. You are told that a_1= 275, n= 16, and that the sum is 8000 so you can solve for d.

 

[r-soy]

see I write two answer see which one is correct :

An = 2a1 + ( n - 1 ) d
a16 = 275(15) d = 80000
4125d = 80000
d = 8000/4125 = 1.9
-------------------------------
-----------------------------
Sn = n/2( 2.a1 ( n - 1 ) d
16/2(2(275)(15) d ) = 8000
8(8250d) = 80000
d = 8000/60000 = 0.12

 

[HallsofIvy]

Neither of those is correct! You have solved for d and the question does not ask for d.