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1. a lecture theatre has a trapezium shaped floor plan so that the number of chairs in successive rows are in arithmetic sequence.the back rows of chairs contain 8 chairs and the front row contains 30. there are 12 rows altogether. 1.find the number of seats in the theatre 2. find the percentage of seats that are in the rear half of the theatre i cant work this out?
2. (Original post by markosheehan)
a lecture theatre has a trapezium shaped floor plan so that the number of chairs in successive rows are in arithmetic sequence.the back rows of chairs contain 8 chairs and the front row contains 30. there are 12 rows altogether. 1.find the number of seats in the theatre 2. find the percentage of seats that are in the rear half of the theatre i cant work this out?
Why not? What have you tried? What part are you stuck on? Show us your attempts.
3. well i tried this. 30-8 =22 seats this has to be spread out across 10 rows as i dont include the first and last. 22/10=2.2 seats extra each row. then i use the formula n/2{2a+ (n-1)d} and i get my answer to be 241.2 and this is not the right answer the right answer is 228
4. (Original post by markosheehan)
a lecture theatre has a trapezium shaped floor plan so that the number of chairs in successive rows are in arithmetic sequence.the back rows of chairs contain 8 chairs and the front row contains 30. there are 12 rows altogether. 1.find the number of seats in the theatre 2. find the percentage of seats that are in the rear half of the theatre i cant work this out?
Let the back row be row 1 and the front row be row 12. Then since the number of chairs in each row forms an arithmetic sequence, we can consider this to be a sequence with first term 8, last term 30, and number of terms = 12. Then use n/2*(a+l) to get 12/2*(8+30) = 6*38=228, as required.

In rear half = In rows 6 to 12 inclusive. Now we do need the common difference of the series, so to work it out, do 8 + 11d = 30 -> d = 2. Thus sum of 6th to 12th rows = 228 - sum from 1st to 5th rows (inclusive)
now using n/2*(2a+(n-1)d) for the sum gives 228 - 5/2(2*8 + 4*2) = 228 - 5/2(24) = 168.
Thus the percentage is 168/228 * 100% = 73.7% (3 s.f.)

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