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Chapter 3: Q14. (page 110)

Use inductive reasoning to predict the next number in each sequence.

1,鈥夆赌夆赌�4,鈥夆赌�9,鈥夆赌�16,鈥夆赌�25,鈥�...

Short Answer

Expert verified

Sequence with next number is 1,鈥夆赌�4,鈥夆赌�9,鈥夆赌�16,鈥夆赌�25,鈥�36炉....

Step by step solution

01

Step 1. Define inductive reasoning.

Inductive reasoning is conclusions based on several past observations.

02

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,

a1=1=12a2=4=22a3=9=32a4=16=42a5=25=52

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

03

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,

a6=36=62.

Therefore, the sequence will be 1,鈥夆赌�4,鈥夆赌�9,鈥夆赌�16,鈥夆赌�25,鈥�36炉....

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