Posted by Stinkrat on Saturday, February 9, 2013 at 4:04pm.
Instructions
Suppose we have a sequence
(1), (2, 3), (4, 5, 6). (7, 8, 9, 10), (11, 12, 13, 14, 15), ...
where (1) is the first element of the sequence, (2, 3) is the second, etc. What is the first number in the 100th element of the sequence? Be sure to do more than answer the problem. Could you use this problem with your students? What grade level would be appropriate? Could you adapt the problem to make it appropriate for at least four different grade levels?

Math  Steve, Saturday, February 9, 2013 at 4:15pm
the sum of the 1st n elements is
1,3,6,10,15,...
it will be a cubic, since it's the sum of n(n+1)/2 for n terms
Sum of 1st n triangular numbers is
n(n+1)(n+2)/6
sum of 1st 99 elements is thus (99)(100)(101)/6 = 166650
So, the 100th element begins with the number 166651
since this involves proof by induction, I'd say algebra 2 would be a good place to present it.

Math  Stinkrat, Saturday, February 9, 2013 at 5:37pm
Thanks Steve
What do you mean by its a cubic?

Math  Steve, Saturday, February 9, 2013 at 11:07pm
hmm. since we're talking about polynomials here, I figured it'd be clear that I meant a 3rddegree polynomial. As opposed to a quadratic or linear.

Math  angel, Sunday, February 10, 2013 at 4:28pm
3000+40,0000

Math  Justin, Monday, February 11, 2013 at 5:21pm
720
Answer This Question
Related Questions
 Math for Educators  The first difference of a sequence is 8, 12, 16, 20,... The...
 Math  A sequence is formed by adding together the corresponding terms of a ...
 Computer Science  MATLAB  One interesting property of a Fibonacci sequence is ...
 Computer Science  MATLAB  I guess it was skipped One interesting property of a...
 MATH  A new sequence is formed by adding together the corresponding terms of a ...
 Algebra  The first element of a geometric sequence is 1 and the common ratio is...
 math  The first and second terms of an exponential sequence (G.P) are ...
 Maths  1..The first 2 terms of a geometric progression are the same as the ...
 math  suppose an arithmetic sequence and a geometric sequence with common ...
 math  in an arithmetic sequence the common difference is equal to 2.the first ...
More Related Questions