Mod 8 Honors Assignment - Sequences and Series Connecting Arithmetic and Geometric Sequences Example: Three numbers form a geometric sequence whose common ratio is 3. If the first is decreased by 1, the second decreased by 3, and the third reduced to 2 less than half its value, the resulting three numbers form an arithmetic sequence. Determine the original three numbers Step 1: Represent the 3 numbers that form a x, 3x, 9x geometric sequence: Step 2: Represent the 3 numbers that form an arithmetic sequence: x - 1, 3x - 3, 5 x - 2 Step 3: Apply the difference property of an arithmetic sequence: ( 3x - 3) -(x-1) - -x-2 - (3x-3) Step 4: Solve for x X - 6 The original numbers are x =6, 3x -18, 9x - 54 Show and Explain all work for each problem 1. Three numbers form a geometric sequence whose common ratio is 0.5. If the first is reduced to 10 more than one quarter its value, the second decreased by 10, and the third increased by 10 more than twice its value, the resulting three numbers form an arithmetic sequence. Determine the original three numbers. 30 points MacBook Air