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

Doorsteptutor material for CBSE/Class-9 Science is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

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

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.

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

Now,

And

Therefore,

Hence, are in G.P.

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

We get,

Or,

which gives

i.e.,

Dividing (2) by (3), we get

Dividing both sides by , we get

Developed by: