Question 78348
<pre>
Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) 	What is r, the ratio between 2 consecutive terms? 
                 a[k+1]
           r =  ________
                  a[k]

                  3              9
             =  _____  = 3,    _____  = 3 , hence r = 3
                  1              3

b) 	Using the formula for the nth term of a geometric sequence, what is the 10th term?

            {{{a[n]}}} = {{{a[1]}}}{{{r^(n-1)}}}
             n = 10, r = 3, {{{a[1]}}}= 1
            {{{a[10]}}} = {{{1 (3^(10-1))}}}
                       = 1 (3^9)
                       = 19683

c) 	Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms? 

                    {{{a[1]}}}({{{r^n - 1}}})
     {{{s[n]}}} =  _____________
                     r - 1
Where r = 3, n = 10, {{{a[1]}}} = 1


                    1 ({{{3^10 - 1}}})
     {{{s[10]}}} =  _____________
                       3 - 1
                 
                   1 (59049 - 1)
              =  ________________
                       2

                  59048
              =  _________
                    2

              =   29524