SOLUTION: Complete the following pattern: 2, 3, 4.5, 6.75, _____, _____:

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Question 308839: Complete the following pattern: 2, 3, 4.5, 6.75, _____, _____:
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
As always goes for easy school problems, look at the differences between numbers. (you do not have to be a genius to remember this simple rule, always try it first if the answer is not obvious)
differences are
1,1.5,2.25
those are powers of 1.5.
So the next number is 6.75%2B1.5%5E3
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: 6.75%2B1.5%5E3 simplifies to 10.125
  • Text form: 6.75+1.5^3 simplifies to 10.125
  • Cartoon (animation) form: simplify_cartoon%28+6.75%2B1.5%5E3+%29
    For tutors: simplify_cartoon( 6.75+1.5^3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION


Look at 6.75%2Bhighlight_red%28+1.5+%29%5Ehighlight_red%28+3+%29.
Replace constants in factor: highlight_red%28+1.5+%29,highlight_red%28+3+%29 with highlight_green%28+3.375+%29
It becomes 6.75%2Bhighlight_green%28+3.375+%29.

Look at highlight_red%28+6.75+%29%2Bhighlight_red%28+3.375+%29.
Replace constants in expression: highlight_red%28+6.75+%29,highlight_red%28+3.375+%29 with highlight_green%28+10.125+%29
It becomes highlight_green%28+10.125+%29.
Result: 10.125

Universal Simplifier and Solver


Done!

The next number is 10.125%2B1.5%5E4
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: 10.125%2B1.5%5E4 simplifies to 15.1875
  • Text form: 10.125+1.5^4 simplifies to 15.1875
  • Cartoon (animation) form: simplify_cartoon%28+10.125%2B1.5%5E4+%29
    For tutors: simplify_cartoon( 10.125+1.5^4 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION


Look at 10.125%2Bhighlight_red%28+1.5+%29%5Ehighlight_red%28+4+%29.
Replace constants in factor: highlight_red%28+1.5+%29,highlight_red%28+4+%29 with highlight_green%28+5.0625+%29
It becomes 10.125%2Bhighlight_green%28+5.0625+%29.

Look at highlight_red%28+10.125+%29%2Bhighlight_red%28+5.0625+%29.
Replace constants in expression: highlight_red%28+10.125+%29,highlight_red%28+5.0625+%29 with highlight_green%28+15.1875+%29
It becomes highlight_green%28+15.1875+%29.
Result: 15.1875

Universal Simplifier and Solver


Done!