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Question

The sequence of all even numbers is a/an ___ arithmetic progression and that of the first 100 odd numbers is a/an  ___ arithmetic progression.
 


A
infinite, infinite
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B
infinite, finite 
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C
finite, infinite 
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D
finite, finite
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Solution

The correct option is B infinite, finite 
An arithmetic progression with finite number of terms is called a finite AP and that with infinite number of terms, an infinite AP.
Consider the sequence of even numbers:
2, 4, 6, 8, 10, ...
Since there are infinite even numbers, the sequence of all even numbers is an infinite arithmetic progression.
On the other hand, the sequence of the first 100 odd numbers is given by 
1, 3, 5, ..., 199, which clearly is a finite arithmetic progression.

Mathematics

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