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)

Question

Katherine Delacruz

Mathematics

5 August, 00:29

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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Prego · Answer 1

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