Arithmetic Sequence Worksheet
what set of seven numbers have the same mean, median, and mode?
i tried it with the same numbers (5,5,5,5,5,5) but it won’t work. I can do it with 5 numbers, but i need it with seven. I really am not that good at math and i left a question blank on my homework worksheet so i’m trying to do the bonus. well if you can’t help me there, at least help me with this question:
State whether this sequence is arithmetic, geometric, or neither. If it is arithmetic or geometric, state what it is being multiplied (or divided) or added (or subtracted!) by. then find the next 3 terms.
9, 3, 1, 1/3…
yes i am blonde, and i embrace it. i am actually a pretty smart cookie compared to some i know… haha 
(A) First, let’s review the definition of mean, median, and mode:
Mean = What we usually refer to as the “average,” i.e. the sum of all numbers divided by the number of instances (7 in this case)
Median = This is the middle number when ordering them in sequential order. In this case, we have an odd number of instances, so it is convenient; the median will be one of the numbers
Mode = This is the number occurring the most frequently
So, if your series is N1, N2, … , N7 (listed in ascending order), we know that Median = N4. For the Mode to be N4, you need at least another number including either N3 or N5 where N3 = N4, or N5 = N4. For the Mean, you can modify the remaining numbers to give you (∑Ni)/7 = N4.
So, your initial try with (5,5,5,5,5,5,5) should work: Median = 5, no issue there. Mode = 5, it is absolutely the most frequently occuring number. Mean = (5+5+5+5+5+5+5)/7 = 35/7 = 5. But it didn’t have to be 5; it could be any value from 1 to ∞.
Other solutions include (1,2,3,3,3,4,5) and any set of the form (N-a,N-b,N,N,N,N+a,N+b). And there are many other combinations.
(B) For your second question, you have a geometric sequence with an initial value of 9 and a factor of 1/3:
9 * 1/3 = 3
3 * 1/3 = 1
1 * 1/3 = 1/3
1/3 * 1/3 = 1/9
1/9 * 1/3 = 1/27
1/27 * 1/3 = 1/81
Peace.
Q3 Arithmetic AP sequences and series solomon worksheet B