Sequences and Series quiz

In an arithmetic sequence, u _{1} = 2 and u_{3} = 8.Find: S _{10}=d = u _{20 }=Find
∑(4i − 3)_{i=1}_{5}^{i=2}_{8}= The first four terms of a sequence are 2,6,18,54... u _{9}=Let S _{n} be the sum of the first n terms of an arithmetic sequence, whose first three terms are u_{1}, u_{2} and u_{3}. It is known that S_{1} = 7, and S_{2} = 18.u _{4}=d = u _{1}=Arturo goes swimming every day. He swims 200 meters in the first day. Each day, he swims 10 meters more than the previous day. He continues for one month (30 days).(a)How far does Arturo swim in the last day of the month?(b)How far does he swim altogether. (a) (b) m m For the series 3+3.3+3.6+3.9+...+63 How many terms are there? The sum is There are terms A geometric sequence u1, u2, u3, ... has u1 = 27 and a sum to infinity of 40½.Find the common ratio of the geometric sequence. ( round to second decimal) Determine if the series diverges or converges. Write D for divergent series and C for convergent series in the boxes provided. 4 + 3 + 2.25 + 1.6875 +... 2 + 4 + 8 + 16 + 32+... 5 - 10 + 20 - 40 + 80+... Evaluate k = 2 10 k ^{2} + 1 =Gwendolyn added the multiples of 3, from 3 to 3750 and found that 3 + 6 + 9 + … + 3750 = s.Calculate s. Ashley and Billie are swimmers training for a competition.(a)Ashley trains for 12 hours in the first week. She decidesto increase the amount of time she spends training by 2 hourseach week. Find the total number of hours she spends trainingduring the first 15 weeks. hours (b)Billie also trains for 12 hours in the first week. She decidesto train for 10% longer each week than the previous week.(i)Find the number of hour she trains for in the third week. hours (ii)Find the total number of hours she spends training duringthe first 15 weeks. hours ( round all answers to whole number) b) 3, 5, 9,17,... a _{n}=a) 5, 7, 9, 11,... a _{n}=c) 0, 3, 8, 15, 24,... a _{n }=d) 1, 4, 7, 10, 13,... a _{n}=Find the explicit formula ( in term of n , use ^ for exponenti.e. 5 ^{n} is written as " 5^ n"):An 81 meter rope is cut into n pieces of increasing lengths that form an arithmetic sequence with a common difference of d meters. Given that the lengths of the shortest and longest pieces are 1.5 meters and 7.5 meters respectively, find the values of n and d. n = d = The mean (average) of the first ten terms of an arithmetic sequence is 6. The mean of the first twenty terms of the arithmetic sequence is 16. Find the value of the 15th term of the sequence. Determine if the sequence is Geometric, Arithmetic or Neither.Write G, A or N in the box provided c) 0.9, 0.875, 0.85, 0.825,... d) 1/2, 2/3, 3/4, 4/5, 5/6,... a) 1, 11,111, 1111,... b) 1, 3/4, 9/16, 27/64,... Write the summation notation and calculate the sum for - 4 -1 + 2 + 5 +...+35 i=1 = c) a) b) Fill in the boxes 3, 2, 5, 8, , ,96 ( Geometric) , , , , ,24, ( Arithmetic) , 23 Find the sum of the arithmetic series 17 + 27 + 37 +...+ 417. b) 2,7,17,37,... Write the recursive formula of the followings, use f(n) and f(n-1) a) 3, 9, 27, 81, ... f(n)= f(n)= |

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