Arithmetic Sequences 2

In Saskatchewan in 1986, there were 1657 beekeepers operating 105 000 colonies. Each colony produced 70 kg of honey. In 2007, the number of beekeepers was reduced to 1048. Assume that the decline in the numbers of beekeepers generates an arithmetic sequence. Determine the change in the number of beekeepers each year from 1986 to 2007.

So, I think you have to solve for d in the equation Tn = T1 + (n-1)d The difference.

1048 = 1657 + (21-1)d
1048 = 1657 + (20)d
1048 = 1677d

This is where I messed up, the answer is suppose to be -29 beekeepers but I get d = .624 which is obviously wrong...

Quote:

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Originally Posted by Mathnood768

1048 = 1657 + (21-1)d
1048 = 1657 + (20)d
1048 = 1677d

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The next line after 1048 = 1657 + (20)d should be 20d = 1048 - 1657.

There is also a remark about the number of years. If T1 means the number of beekeepers in 1986, then we count year 1986 as number 1. Then year 2007 would be number 2007 - 1986 + 1 = 22. Why +1? E.g., year 1987 would be number 2 and 1987 - 1986 = 1. Therefore, n = 22 and you need to divide the difference in the number of beekeepers by n - 1, i.e., 21.