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...
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