Help with Implicit Formula HW: 3, 9, 81, 65...

In summary, The pattern follows a rule where each number is squared to get the next number, except for 65 and 61 which are swapped. The implicit formula would be Xn squared, with the exception of 65 and 61 being swapped.
  • #1
Master7731
14
0

Homework Statement



I have to find an implicit rule for this pattern, Can Someone please help me?

3, 9, 81, 65, 61, 37,... and so on

Homework Equations



Im stuck not sure how to approach and therefore get a rule

The Attempt at a Solution



I tried using the arithmetic and geometric formulas but I am not getting anywhere
 
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  • #2
Hi Master7731! :smile:

Hint: what's 81 squared ? :wink:
 
  • #3
i understand the 3,9,81, as it increase by the square of the previous number part but then it goes does to 65 which i dun understand at all
 
  • #4
Is the problem copied down correctly? Are you sure there is a comma between 65 and 61? If so, does it give you any numbers after 37?
 
  • #5
Master7731 said:
i understand the 3,9,81, as it increase by the square of the previous number part but then it goes does to 65 which i dun understand at all

Hint: what's 81 squared ?
 
  • #6
omg thanks so much tiny-tim so i get it 81 squared is 6761 and 61 squared if 3721 but evne so i been trying to write an equation with no luck as its supposed to be in an implicit formula, so is it like Xn squared but then i dunt know what to write
 
  • #7
Master7731 said:
omg thanks so much tiny-tim so i get it 81 squared is 6761 …

:biggrin: 6561, actually! :rolleyes:
 

1. What is an implicit formula?

An implicit formula is a mathematical equation that expresses the relationship between two or more variables without explicitly solving for one variable in terms of the others. In other words, the formula does not directly state the dependent variable, but rather implies its existence through the relationship with other variables.

2. How do I solve an implicit formula?

Solving an implicit formula can be done by isolating the dependent variable and using algebraic techniques to manipulate the equation. This may involve expanding, factoring, or rearranging terms to eventually solve for the variable of interest.

3. What is the difference between an implicit and explicit formula?

An explicit formula directly states the dependent variable in terms of the independent variable(s), while an implicit formula does not. Explicit formulas are typically easier to solve and manipulate, while implicit formulas can be more complex and require additional steps to solve for the dependent variable.

4. How do I know if a formula is implicit or explicit?

A formula is implicit if it does not explicitly state the dependent variable, but rather implies its existence through the relationship with other variables. An explicit formula, on the other hand, directly states the dependent variable. Sometimes, the form of the equation can also indicate whether it is implicit or explicit.

5. Can you provide an example of an implicit formula?

One example of an implicit formula is the equation for a circle: x2 + y2 = r2, where x and y are the coordinates of a point on the circle and r is the radius. This formula does not explicitly state the dependent variable, but rather relates it to the independent variables x and y.

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