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High School Mathematics - 23.7 Sum of Geometric Series - Using Formula

 Sn = a1(1 - rn)/(1 - r) where r is the common ratio Sn is the sum of the first n terms in a sequence a1 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: a1 = 4 r = 2 a10 = a1 x r9 = 4 . 29 = 2048 Therefore: S10 = 4(1-210)/(1 - 2) = 4 . 1023 = 4092 Example: Find S6 for the sequence: 3 x 4n-1 we need to know a1, n, and r. a1 = 3 x 41-1 = 3 x 40 = 3 x 1 = 3 a2 = 3 x 42-1 = 3 x 41 = 3 x 4 = 12 r = a2/a1 = 12/3 = 4 Since we are being asked to find S6, n is 6. Formula: Sn = a1(1 - rn)/(1 - r) = 3(1 - 46)/(1 - 4)= 4095 Directions: Find the sum of the geometic series. Also write at least 5 examples of your own.
 Q 1: Find the sum of the series: 1 + 2 + 22+ 23+ 24........+ 29 is 123414001023 Q 2: Find the sum of the first 10 terms of: 4-2+1-1/2+......2 85/1283 87/1282 115/158 Q 3: Find the sum of the first 7 terms of 12 + 36 + 108 + 324 + . . . 290011499013116 Q 4: Find the sum of the first 7 terms of: 1 + x + x2+ x3+ ........x7 - 1/x-1x6 - 1/1-x1 - x7/x-1 Q 5: Find the sum of the first 8 terms of: 4 + 2 + 1 + 1/2 + .....8 12/136 23/247 31/32 Q 6: Find the sum of the first 6 terms of the series: 2+6+18+54+162+........+13122196822345113456 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!