1.7 Sum of the First n Terms of a Geometric Progression

1.7 Sum of the First n Terms of Geometric Progressions

(F) Sum of the First n Terms of Geometric Progressions
   S n = a( r n 1) r1 , r>1      S n = a(1 r n ) 1r , r<1
a = first term
r = common ratio
n = number of term
Sn = sum of the first n terms

Example 1:
Find the sum of each of the following geometric progressions.
(a) 1, 2, 4, ...  up to the first 7 terms
(b) 9, 3,   1,   ,   ...    up to the first 6 terms
(c) 12, 3, ...., 3 64  [Smart TIPS: You can find n if you know the last term]

Solution: