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Chapter 3: Q12. (page 110)

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

2,鈥夆赌�鈭�4,鈥夆赌�8,鈥夆赌�鈭�16,鈥夆赌�....

Short Answer

Expert verified

Sequence with next number is 2,鈥夆赌�鈭�4,鈥夆赌�8,鈥夆赌�鈭�16,鈥夆赌�32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 sequence 2,鈥夆赌�鈭�4,鈥夆赌�8,鈥夆赌�鈭�16,鈥夆赌�...reason inductively that is., we can conclude based on past observations

As,

a1=2a2=2脳鈭�2=鈭�4a3=鈭�4脳鈭�2=8a4=8脳鈭�2=鈭�16

So, the pattern of the sequence is that every term is getting multiplied by 鈥�2 to obtain the next term.

03

Step 3. Predict the next number of the sequence.

Since the pattern of the sequence is that every term is getting multiplied by 鈥�2 to obtain the next term, therefore, the next two terms of the sequence will be,

a5=鈭�16脳鈭�2=32.

Therefore, the sequence will be 2,鈥夆赌�鈭�4,鈥夆赌�8,鈥夆赌�鈭�16,鈥夆赌�32炉....

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