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Chapter 3: Q14. (page 113)

Predict the next two numbers in the sequence7,  9,  11,  13, ...

Short Answer

Expert verified

Sequence with next two numbers is 7,  9,  11,  13 15¯, 17¯, .....

Step by step solution

01

Step 1. Define deductive and inductive reasoning.

Deductive reasoning is conclusions based on accepted statements like a theorem, postulate, facts etc.

Inductive reasoning is conclusions based on several past observations.

02

Step 2. Look for a pattern.

First term of the series is 7.

a1=7

Second term of the series is 9.

a2=9

Third term of the series is 11.

a3=11

And so on,

Determine the common difference as follows:

a2−a1=9−7=2a3−a2=11−9=2a4−a3=13−11=2

Thus, in each case, common difference (d) is same.

Hence, the series is AP (Arithmetic progression) series.

03

Step 3. Predict the next two numbers of the sequence.

Next two terms of the series is calculated as follows:

a5=a4+d=13+2=15a6=a5+d=15+2=17

Thus, the next two terms of the series are 15 and 17.

Therefore, sequence with next two numbers is 7,  9,  11,  13 15¯, 17¯, .....

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