The sum of the first terms n in the infinite geometric sequence {1/4, 1/8, 1/16, ..} is 15/32. Find n.
+23246 The formula for the sum of a finite geometric series is: Sum = [ a · ( 1 - rn ) ] / (1 - r)
For this problem, the first term a = 1/4.
For this problem, the common ratio r = 1/2.
So: 15/32 = [ ¼ · ( 1 - ½n ) ] / (1 - ½)
15/32 = [ ¼ · ( 1 - ½n ) ] / (½)
15/32 = ½ · ( 1 - ½n )
15/16 = 1 - ½n
-1/16 = - ½n
1/16 = ½n
n = 4
