CBSE Class 10-Mathematics: Chapter –5 Arithmetic Progressions Part 9

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Question 7:

How many multiples of lie between and ?

Answer:

The odd numbers between and are

It is an arithmetic progression because the difference between consecutive terms is constant.

First term , Common difference ,

Last term

We do not know how many odd numbers are present between and .

Therefore, we need to find n first.

Using formula , to find nth term of arithmetic progression, we get

Applying formula, to find sum of n terms of AP, we get

Question 8:

Which term of the AP: is its first negative term?

Answer:

Given:

Here

Now,

For the first negative term,

is an integer and

Hence, the first negative term is term

Question 9:

The sum of the third and the seventh terms of an AP is and their product is . Find the sum of sixteen terms of the AP.

Answer:

Let the AP be

Then,

Also

Taking

Taking