##### finding an equation from a table

label Algebra
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a table of x= 1, 2, 3, 4, 5 and y= 1, 2, 4, 8. I need to find the equation to this

Oct 12th, 2015

Given

x     y

1     1

2     2

3      4

4      8     and so on

equation to represent this table is,   y(x) = (sum of all y values from 1 to x-1) + 1

or, y(x) = (y(1) + y(2) + .......+ y(x-1)) + 1

consider x = 3,

y(3) = (y(1) + y(2)) + 1

here, y(1) = 1 and y(2) = 2

so, y(3) = (1+2) + 1   =  4            this value is ame as the given value, hence equation is correct for x = 3

consider x = 4,

y(4) = (y(1) + y(2) + y(3) ) + 1

y(4) = (1+ 2 + 3 ) + 1  = 8          this value is ame as the given value, hence equation is correct for x = 4

in a similar way, this equation will be correct for all further values of x.

so, the final equation is :   y(x) = (y(1) + y(2) + .......+ y(x-1)) + 1

Please let me know if you need any clarification. I'm always happy to answer your questions. Kindly best this answer if it has helped you.
Oct 12th, 2015

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Oct 12th, 2015
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Oct 12th, 2015
Sep 23rd, 2017
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