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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)

Q: Could you please Give me examples of arithmetic progressions?

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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.

could also be negative

Neither. It could be polynomial (of order 4 or more) or something else.

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It was the first calculator that could perform all four arithmetic operations: addition, subtraction, multiplication and division.

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could you please give me examples of your work

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.

He could do arithmetic in his head *really fast. *optional

I don't know what you are referring to. You could be referring to transits or progressions which are used for astrological forecasts.

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Sure! Examples of colonization include the British colonization of India, the Spanish colonization of Latin America, and the French colonization of Algeria.

The distinguished Scottish mathematician, John Napier, provided science and mathematics with a vastly improved and rapid method of notation and calculation. He founded the use of logarithm, a way to turm multiplication into addition, and Division into subtraction. Thus, he facilitated a computational system whereby roots, products and quotients could easily be determined from tables showing powers of a fixed number used as a base. The basis for this computation is the relationship between arithmetic progressions and geometric progressions. Scientists and mathematicians continued to use logarithms until the invention of the calculator and the computer, which proved to be more efficient tools.

The Devil's Arithmetic starring Kristen Dunst is rated TV-14. This could mean PG-13 or R.

You take the difference between the second and first numbers.Then take the difference between the third and second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Take the difference between the fourth and third second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Keep checking until you think the differences are all the same.That being the case it is an arithmetic sequence.If you have a position to value rule that is linear then it is an arithmetic sequence.

A complex formula in Excel could have many arithmetic operators in it. There are many things that make a formula complex, so a formula with just one arithmetic operator or even no arithmentic operators could be complex too, depending on what it does.

could also be negative

Could you please open that door for the woman in the wheelchair? He could run a mile in under 7 minutes. Bailey could eat peanut butter, but James couldn't because of a severe allergy.