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Chapter 3: Q13. (page 110)

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

7,鈥夆赌夆赌�12,鈥夆赌�17,鈥夆赌�22,鈥夆赌�27,鈥�...

Short Answer

Expert verified

Sequence with next number is 7,鈥夆赌夆赌�12,鈥夆赌�17,鈥夆赌�22,鈥夆赌�27,鈥�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 sequences 7,12,17,22,27,... reason inductively that is., we can conclude based on past observations

As,

a1=7a2=7+5=12a3=12+5=17a4=17+5=22a5=22+5=27

So, the pattern of the sequence is that 5 is getting added in every term to obtain the next term.

03

Step 3. Predict the next number of the sequence.

Since, the pattern of the sequence is that 5 is getting added in every term to obtain the next term, therefore, the next term of the sequence will be,

a6=27+5=32.

Therefore, the sequence will be 7,鈥夆赌夆赌�12,鈥夆赌�17,鈥夆赌�22,鈥夆赌�27,鈥�32炉....

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