CBSE Class 10-Mathematics: Chapter – 5 Arithmetic Progressions Part 14 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 3:

If the third and the ninth terms of an AP are and respectively, which term of this AP is zero?

It is given that 3rd and 9th term of AP are 4 and respectively.

It means and

Using formula , to find term of arithmetic progression,

These are equations in two variables.

Using equation , we can say that

Putting value of a in other equation ,

Putting value of in equation ,

Therefore, first term and Common Difference

We want to know which term is equal to zero.

Using formula to find term of arithmetic progression,

Therefore, term is equal to .

Question 4:

Two AP՚s have the same common difference. The difference between their terms is , what is the difference between their terms.

Let first term of 1st AP

Let first term of 2nd

It is given that their common difference is same.

Let their common difference be .

It is given that difference between their terms is .

Using formula , to find nth term of arithmetic progression,

We want to find difference between their

1000th terms which means we want to calculate:

Putting equation (1) in the above equation,

Therefore, difference between their 1000th terms would be equal to 100.

Question 5:

How many three-digit numbers are divisible by 7?

We have AP starting from because it is the first three-digit number divisible by .

AP will end at because it is the last three-digit number divisible by .

Therefore, we have AP of the form

Let is the nth term of AP.

We need to find n here.

First term , Common difference

Using formula , to find term of arithmetic progression,

It means is the term of AP.

Therefore, there are terms in AP.

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