Question 4: (last question)
a) Three numbers whose product is 216 are in geometric progression. If 1, 4, 8 are subtracted from them respectively the results are in arithmetic progression. Find the numbers (6 marks)
b) A<sub>n</sub> and B<sub>n</sub> are two series given by:
A<sub>n</sub> = 1<sup>2</sup> + 5<sup>2</sup> + 9<sup>2</sup> + 13<sup>2</sup> + ....... + (4n-3)<sup>2</sup>
B<sub>n</sub> = 3<sup>2</sup> + 7<sup>2</sup> + 11<sup>2</sup> + 15<sup>2</sup> + ....... for n = 1, 2, 3......
(i) Find the n<sup>th</sup> term of B<sub>n</sub>. (1 mark)
(ii) If S<sub>2n</sub> = A<sub>n</sub> - B<sub>n</sub> prove that If S<sub>2n</sub> = -8n<sup>2</sup> (3 marks)
(iii) Hence, or otherwise, evaluate
101<sup>2</sup> - 103<sup>2</sup> + 105<sup>2</sup> - 107<sup>2</sup> + ...... + 2001<sup>2</sup> - 2003<sup>2</sup> (2 marks)
I got part a) of Q4. I was the only one in my class to get it, but 2 4U students also got it.
I also got part b) (i), but I couldn't get the rest. I ran out of time.
IMO, a) was pretty easy, but the last 2 parts of b) were fairly tough. Although the teacher said it was actually a fairly easy question. Time was the biggest factor in my exam. We had 60 minutes to complete it. (4 Qs - 12, 13, 13, 12 = 50 marks)
I got 80% for the exam: 12, 13, 8 and 7 respectively. Other two got 44 and 46 I think (not in my class so I don't know). If you haven't read my other post, these two guys got 49/50 for 3U last year, but want to come first in the state so they're doing it again.
(apparently).