Question

For the following exercises, express each geometric sum using summation notation. 

1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187

Answer 1

Consider the following geometric series:

1 + 3 + 9 + 27 + 81 + 242 + 729 + 2187

 

First term of above geometric series is a1 = 1

Common ratio of above series will be,

r = a2/a1

   = 3/1

   = 3

 

Use the explicit formula of a geometric sequence,

an = a1 × rn-1 ...... (1)

 

Substitute a1 = 1 and r = 3, the explicit formula for above sequence is,

an = 1 × 3n-1

      = 3n-1

 

Count the number of terms in the above series. There are 8 terms. So, lower limit of above sum is n = 1 and upper limit is n = 8.

 

Now, use the summation notation to express the sum of terms as follows,

Sn = 8Σn=1(3n-1)

Sn = 8Σn=1(3n-1)