Sequences

1. In a cinema, there are 32 seatsin the first row. The number of seats in each row, except the first row, ismore than that in its preceding row by 2. Let T(n) denote the number seats inthe nth row, and k be the total number of rows in the cinema. Is the sequence T(1), T(2),T(3),…,T(k) an arithmetic sequence?Briefly your answer. ANS: Yes 2. Fanny is playing with woodenblocks. She stacks up the wooden block in the following way: Each layer has 3wooden blocks less than the layer below it. If there are 25 wooden blocks in the 9th layer countingfrom the bottom, find the maximum number of layers of wooden blocks that Fannycan stack up. ANS: 17 3. There are 3 yeast cells in aflask initially. It is known that the number of yeast cells doubles every 5minutes. Let T(n) be the number of yeast cells in the flask after n 5-minuteintervals. a) Is the sequence T(1), T(2),T(3),…an arithmetic sequence or a geometric sequence? Briefly explain your answer. ANS: geometric sequenceb) Find T(n). ANS: T(n)=3(2)^n 4. Mr. Lee ‘s monthly salary is $M in 2005. It increases at a constant rate of r% per year. It is known that Mr.Lee saves 20% of his monthly salary each month. Let $T(n) be his monthlysavings in the nth year(i.e. $ T(1) is his monthly savings in 2005).a) Express T(n) in terms of M andr. ANS: T(n) =0.2M(1+r%)^n-1b) If T(2) =2160 and T(4) =2520,when will his monthly savings be first greater than $3100? ANS: 2011 How can I findthe answers? Thanks!