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Use inductive reasoning to predict the next line in the pattern. Then perform the arithmetic to determine whether your conjecture is correct. 8 (5) = 10 (5 - 1) 8 (5) + 8 (25) = 10 (25 - 1) 8 (5) + 8 (25) + 8 (125) = 10 (125 - 1) 8 (5) + 8 (25) + 8 (125) + 8 (625) = 10 (625 - 1)

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  1. 5 August, 00:48
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    8 (5) + 8 (25) + 8 (125) + 8 (625) + 8 (3125) = 10 (3125 - 1) = 31240

    Hence proved Conjecture is correct

    L. H. S=R. H. S

    Step-by-step explanation:

    Consider the pattern:

    8 (5) = 10 (5-1) = 40

    8 (5) + 8 (25) = 10 (25 - 1) = 240

    8 (5) + 8 (25) + 8 (125) = 10 (125 - 1) = 1240

    8 (5) + 8 (25) + 8 (125) + 8 (625) = 10 (625 - 1) = 6240

    According to inductive reasoning next term of pattern will become:

    8 (5) + 8 (25) + 8 (125) + 8 (625) + 8 (3125) = 10 (3125 - 1) = 31240

    Checking whether conjecture is correct or not:

    Consider L. H. S:

    8 (5) + 8 (25) + 8 (125) + 8 (625) + 8 (3125)

    40+200+1000+5000+25000

    31240

    R. H. S:

    31240

    Hence proved Conjecture is correct

    L. H. S=R. H. S
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