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1,11,21,31,41, ... goes on forever. The common difference is 10. Start with the number 1 and since 10 is the common difference, add 10, you have 11, now add 11 again and you have 21, keep going like this. The sum S of the first n values of a finite sequence is given by the formula: S = 1/2(a1 + an)n, where a1 is the first term and an the last. So in the example I gave, take the first 3 numbers, 1, 11 and 21. S is the sum of them which we know is 33 just by adding 1 +11+21 Now using the formula, S=1/2[(1+21)3]=1/2(66)=33 as we expected. Here is the formula for the nth term an = 1/2(an-1 + an+1)
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What is a rectangular number sequence?
A rectangular number sequence is the sequence of numbers of counters needed to construct a sequence of rectangles, where the dimensions of the sides of the rectangles are whole numbers and change in a regular way. The individual sequences representing the sides are usually arithmetic progressions, but could in principle be given by difference equations, geometric progressions, or functions of the dimensions of the sides of previous rectangles in the sequence.
The common difference in an arithmetic sequence is a positive number?
could also be negative
Is an arithmetic mean a weighted mean or a weighted mean an arithmetic mean?
The arithmetic mean is a weighted mean where each observation is given the same weight.
Is 2 3 5 8 15 geometric or arithmetic?
Neither. It could be polynomial (of order 4 or more) or something else.
What was mathematical operation was stepped reckoner supposed to perfrom?
It was the first calculator that could perform all four arithmetic operations: addition, subtraction, multiplication and division.
