What is the equation for the data? And how did you get it?

Question

I don't understand how you find the equation.

x- 0 1 2 3 4
y- 2 6 18 54 162

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Answer 1 · 2018-07-24T08:19:30

$y = 2 \cdot 3^{x}$ $y=2*3^x$

It is observed that while values of $x$ $x$ are in arithmetic sequence,

where $x = a_{n} = n - 1$ $x=a_n=n-1$ , which gives us $n = x + 1$ $n=x+1$

values of $y$ $y$ are in geometric sequence,

where $y = g_{n} = 2 \cdot 3^{n - 1}$ $y=g_n=2*3^(n-1)$ - let us call it (A)

Hence relation is $y = 2 \cdot 3^{x}$ $y=2*3^x$

This is obtained by putting $n = x + 1$ $n=x+1$ in (A) .