CBSE Class 10-Mathematics: Chapter –5 Arithmetic Progressions Part 14
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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?
Answer:
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.
Answer:
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?
Answer:
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 meansis the term of AP.
Therefore, there are terms in AP.