What is the sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...? a. 3 b. 1 c. 3/4 D.3/7 Geometric Sequence Finding the sum The sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ . ..is 3/7. Solution: Geometric Series Sum Formula: S = a₁/1 - r Given: a₁ = 3/4 a₂ = -9/16 a₃ = 27/64 a₄ = -81/256 1. Find the common ratio. a_n = a₁r ⁿ ⁻ ¹ a₂ = a₁r ⁿ ⁻ ¹ -9/16 = 3/4 r ² ⁻ ¹ -9/16 = 3/4 r 2. Divide both sides of the equation by 3/4 to find r. -9/16/3/4 = 3/4 r/3/4 (-9/16)(4/3) = r -36/48 = r -3/4 = r 3. Using r = -3/4, find the sum of the infinite geometric series 3/4 -9/16 +27/64 -81/256+ ... S = a₁/1 – r S = 3/4/1 – (-3/4) S = 3/4/1 + ¾ S = 3/4/4/4 + 3/4 S = 3/4/7/4 S = (3/4)(4/7) S = 12/28 S = 3/7 4. Therefore, the sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7. Defin...
What is the next number? What is the 12th number? 1, 3, 9, 27, 81, _____ Answer: The next number is 243. Therefore, the sequence is 1, 3, 9, 27, 81, 243 . Step-by-step explanation: To determine the answer, you have to find the rule or pattern that is being applied in the sequence. If you could notice, the next number is always the product of 3 and the previous number. For example, 81 is the product of 3 and 27. 27 is the product of 3 and 9. 3 is the product of 3 and 1. Therefore, the next number in the sequence should be the product of 3 and 81. 81 x 3 = 243. The answer is 243, and the complete sequence is 1, 3, 9, 27, 81, 243 . That is the answer for the given question. To know more about the topic, here are other helpful links that you can use: To know more about what an arithmetic sequence means, you can check this out: brainly.ph/question/552449 and brainly.ph/question/581574 To discover more about the formula in finding out missing terms in an arithmetic sequence, you can ...
Alfred Wegener is a German scientist who hypothesized that the Earth was once made up of a single large landmass called Pangaea. Which of the following theories did Wegener propose? a. Continental Drift Theory b. Continental Shift Theory c. Plate Tectonics d. Seafloor Spreading Theory Answer: The correct answer is letter a. Continental Drift Theory. Explanation: The theory that Alfred Wegener propose is the Continental Drift Theory. It Hypothesized that continents were once a large supercontinent that drifted apart from each other. This was largely unaccepted in the northern hemisphere where geologists don not believe that rock movements of that type could happen. This was widely accepted by the geologists in the southern hemisphere. Some of the proofs that Wegener used in the continental drift theory were: The fit of the continents. Distribution of fossils wherein same species were discovered on different continents. Glaciation on some continents at same period in th...
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