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A recursive definition is any definition that uses the thing to be defined as part of the definition. A recursive formula, or function, is a related formula or function. A recursive function uses the function itself in the definition. For example: The factorial function, written n!, is defined as the product of all the numbers, from 1 to the number (in this case "n"). For example, the factorial of 4, written 4!, is equal to 1 x 2 x 3 x 4. This can also be defined as follows: 0! = 1 For any "n" > 0, n! = n x (n-1)! For example, according to this definition, the factorial of 4 is the same as 4 times the factorial of 3. Try it out - apply the recursive formula, until you get to the base case. Note that a base case is necessary; otherwise, the recursion would never end.
Yes. The next two numbers would be 49 & 58. This is because, from the first number, the pattern repeats by adding 10 then 9. So - 39+19 is 49, and 49+9=58.
The base is the lower-left number, in this case, 8.
10 is the base in this case.
Base times height. This is the same formula as for a rectangle, however, in the case of a parallelogram, the base is one of the sides, and the height has to be measured perpendicular to that base.