NCERT Class 11-Math՚s: Chapter – 9 Sequence and Series Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 6:

The product of three numbers in A. P. is , and the largest number is times the smallest. Find the numbers.


Let the three numbers in A. P. be


Now, since the largest number is times the smallest, i.e.. ,


Substituting this value of in , we get


Hence, the three numbers are .

Question 7:

Show that and consecutive terms of an A. P. , if and are in A. P.


The terms and will be in A. P. if

Which is true, since are in A. P. Hence are in A. P.

Question 8:

If are in G. P. , prove that are also in G. P.


Let be the common ratio of the given G. P. Then




Hence, are in G. P.

Long Answer Type

Question 9:

If the sum of terms of an A. P. is equal to the sum of either the next terms or the next terms, then prove that


Let the A. P. be , … We are given

Adding on both sides of , we get


Putting in the above equation, we get

Similarly, if

Adding on both sides

We get,


which gives

i.e.. ,

Dividing (2) by (3) , we get

Dividing both sides by , we get

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