Chapter 3: Q14. (page 110)

Use inductive reasoning to predict the next number in each sequence.
$1, 4, 9, 16, 25, ...$

Short Answer

Expert verified

Sequence with next number is $1, 4, 9, 16, 25, \underline{36} ...$ .

Step by step solution

Step 1. Define inductive reasoning.

Inductive reasoning is conclusions based on several past observations.

Step 2. Look for a pattern.

While looking for a pattern in the sequences 1,4,9,16,25,... reason inductively that is., we can conclude based on past observations

As,

$\begin{array}{l} a_{1} = 1 = 1^{2} \\ a_{2} = 4 = 2^{2} \\ a_{3} = 9 = 3^{2} \\ a_{4} = 16 = 4^{2} \\ a_{5} = 25 = 5^{2} \end{array}$

So, the pattern of the sequence is the sequence of squares of natural numbers 1,2,3,4,5 and so on in order.

Step 3. Predict the next number of the sequence.

Since the pattern of the sequence is the sequence of squares of natural numbers 1,2,3,4,5 and so on in order., therefore, the next term of the sequence will be,

$a_{6} = 36 = 6^{2}$ .

Therefore, the sequence will be $1, 4, 9, 16, 25, \underline{36} ...$ .

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Use inductive reasoning to predict the next number in each sequence.
$1, 4, 9, 16, 25, ...$

Short Answer

Step by step solution

Step 1. Define inductive reasoning.

Step 2. Look for a pattern.

Step 3. Predict the next number of the sequence.

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Use inductive reasoning to predict the next number in each sequence.1, 4, 9, 16, 25, ...

Short Answer

Step by step solution

Step 1. Define inductive reasoning.

Step 2. Look for a pattern.

Step 3. Predict the next number of the sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Statistics

Pure Maths

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Use inductive reasoning to predict the next number in each sequence.
$1, 4, 9, 16, 25, ...$