
State True or False. If , , are in A.P., then , , are also in A.P.
.
.
Answer
537.9k+ views
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.
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Questions & Answers - Ask your doubts

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Science: Engaging Questions & Answers for Success

Trending doubts
A boat goes 24 km upstream and 28 km downstream in class 10 maths CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What is the full form of POSCO class 10 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Discuss the main reasons for poverty in India
