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

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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

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