
S_{n} = a_{1}(1  r^{n})/(1  r) where r is the common ratio S_{n} is the sum of the first n terms in a sequence a_{1} is the first term in the sequence r is the common ratio in the geometric sequence n is the number of terms you are adding Example: Find the sum of the first 10 terms of the geometric series: 4, 8, 16, 32, 64, . . . Solution: a_{1} = 4 r = 2 a_{10} = a_{1} x r^{9} = 4 . 2^{9} = 2048 Therefore: S_{10} = 4(1210)/(1  2) = 4 . 1023 = 4092 Example: Find S_{6} for the sequence: 3 x 4^{n1} we need to know a_{1}, n, and r. a_{1} = 3 x 4^{11} = 3 x 4^{0} = 3 x 1 = 3 a_{2} = 3 x 4^{21} = 3 x 4^{1} = 3 x 4 = 12 r = a_{2}/a_{1} = 12/3 = 4 Since we are being asked to find S_{6}, n is 6. Formula: S_{n} = a_{1}(1  r^{n})/(1  r) = 3(1  4^{6})/(1  4)= 4095 Directions: Find the sum of the geometic series. Also write at least 5 examples of your own. 