
State True or False. If , , are in A.P., then , , are also in A.P.
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Answer
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Hint: The above problem is related to arithmetic progression. First, we should be able to define an arithmetic sequence. After that its properties can be used to solve the above problem.
Arithmetic Progression is a sequence of numbers such that the difference of any two consecutive numbers is constant.
General term of an A.P. is given by:
Where is the first term of the A.P. sequence and is known as the common difference.
Given in the problem, , , are in A.P.
First term
Second term
Third term
……………………………….. (1)
Here is the common difference.
Since we need to check whether , , are in A.P. or not.
We need to find the common difference of the consecutive terms.
Using equation (1) in above, we get
………………………….(2)
Similarly,
………………...(3)
From (2) and (3) , the common difference of the consecutive terms is equal.
, , are in A.P.
Hence option is the correct answer.
Note: While solving problems related to A. P like above, always try to first write the general term of the A.P. sequence. It is to be observed that if each term of an A.P. is added with a fixed number, then the new obtained sequence is also in A.P.
Arithmetic Progression is a sequence of numbers such that the difference of any two consecutive numbers is constant.
General
Where
Given in the problem,
Here
Since we need to check whether
We need to find the common difference of the consecutive terms.
Using equation (1) in above, we get
Similarly,
From (2) and (3) , the common difference of the consecutive terms is equal.
Hence option
Note: While solving problems related to A. P like above, always try to first write the general term of the A.P. sequence. It is to be observed that if each term of an A.P. is added with a fixed number, then the new obtained sequence is also in A.P.
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