Question 1020019
The first term {{{g[1] = 2}}}, the nth term is {{{g[n]}}} = 2,048.
The sum of the first n terms of a geometric sequence is given by the formula 

{{{S[n] = (g[1] - g[n]*r)/(1-r)}}}

After substitution, 

{{{2730 = (2-2048r)/(1-r)}}}

<==> 2730 - 2730r = 2 - 2,048r, after cross-multiplying.
<==> 2,728 = 682r
<==> {{{highlight(r = 4)}}}, the common ratio (c.r.)

Now from the formula for the nth term of a gp, {{{g[n] = g[1]*r^(n-1)}}},

we get

{{{2048 = 2*4^(n-1)}}}, and we proceed to determine the value of n.
<==> {{{1024 = 4^(n-1) = 2^(2n-2)}}}
==> {{{log(2,1024) = log(2,2^(2n-2))}}}
==> 10 = 2n - 2
==> 12 = 2n
==> {{{highlight(n = 6)}}}, the number of terms added in the sequence, 
and the problem is solved.