Question

Use inductive reasoning to predict the next line in the sequence of computations. Use a calculator...

Use inductive reasoning to predict the next line in the sequence of computations. Use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct.

3=1x3

3+7=2x5

3+7+11=3x7

Homework Answers

Answer #1

The expressions on the left hand side are 3, 3+7, 3+7+11 ,… It may be observed that 7-3 = 4 and 11-7 = 4. Hence the next expressions on the left hand side should be 3+7+11+15, 3+7+11+15+19 and so on.

The expressions on the right hand side are1x3, 2x5, 3x7,… It may be observed that 1,2,3,.. are the natural numbers and 3,5,7,.. is anarithmetic series beginning with 3 and with a common f=difference 2. Hence the next expressions on the left hand side should be 4x9, 5x11 etc.

Thus, 3=1x3

3+7=2x5

3+7+11=3x7

3+7+11+15 = 4x9

3+7+11+15+19 =5x11

etc.

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