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*3^x#

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

where #x=a_n=n-1#, which gives us #n=x+1#

values of #y# are in geometric sequence,

where #y=g_n=2*3^(n-1)# - let us call it (A)

Hence relation is #y=2*3^x#

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