# NCERT Class 11-Math's: Chapter –9 Sequence and Series Part 3

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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