1. A 16-team bowling league has 800,000 to be awarded as prize money. If the last-placed team is awarded 12,500 in prize money and the award increases by a constant amount for each successive finishing place, how much will the first-placed team receive?
2. In Museum A, a stamp collection is valued at 50,000 in 2014 and its value increases by 2,500 annually. In Museum B, the same stamp collection is valued at 45,000 in 2013 and its value increases by 2,750 annually. Which museum will the stamp collection have a higher value in 2025?
1. Use the sum of n terms of an arithmetic sequence
sum = (n/2)(first + last)
(16/2)(first + 12500) = 800000
divide by 8
first + 12500 = 80000
first = 80000-12500 = 67500
2.
museum A:
a = 50,000 , d = 2500
museum B:
a = 45,000 , d = 2750
find term(12) or a+11d for each one
notice: we must follow the correct patter, so 12 terms
t1 -- 2014 ----> 14-1 = 13
t2 -- 2015 ----> 15-2 = 13
...
t12 -- 2025 ---> 25-12 = 13