Question 87237
a)
The ratio r is the factor to get from term to term. So to find r, simply pick any term and divide it by the previous term:
{{{r=27/9=3}}} Divide the term of 27 by 9

So the ratio is
{{{r=3}}}


b)
The sequence is multiplying by a factor of 3 each term, so the sequence is {{{3^n}}}
This means the 10th term is
{{{3^9=19683}}}(let n=9, remember n=0 is the 1st term)

So the 10th term is 19,683



c)
The sum of a geometric series is
{{{S=a(1-r^n)/(1-r)}}}where a=1
{{{S=(1-3^10)/(1-3)}}} Plug in {{{r=3}}} and {{{n=10}}}
{{{S=(1-59049)/(-2)}}} Evaluate {{{3^10}}}
{{{S=(-59048)/(-2)}}} Subtract
{{{S=29524}}} Divide

So the sum of the first ten terms is 29,524