# 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.

**Answer**:

Let the three numbers in A. P. be

Now

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

Therefore,

Substituting this value of in , we get

And

Hence, the three numbers are .

**Question 7**:

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

**Answer**:

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.

**Answer**:

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

Now,

And

Therefore,

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

**Solution**:

Let the A. P. be , … We are given

Adding on both sides of , we get

Therefore,

Putting in the above equation, we get

Similarly, if

Adding on both sides

We get,

Or,

which gives

i.e.. ,

Dividing (2) by (3) , we get

Dividing both sides by , we get