Question

3. How
many three-digit numbers are divisible by 7?
​

Answer 1

Answer:

128 three digit numbers

Step-by-step explanation:

We have AP starting from 105 because it is the first three digit number divisible by 7.

AP will end at 994 because it is the last three digit number divisible by 7.

Therefore, we have AP of the form 105, 112, 119…, 994

994 is the nth term of AP.

We need to find n here.

First term = a = 105, Common difference = d = 112 – 105 = 7

Using formula , to find nth term of arithmetic progression,

⇒994 = 105 + (n − 1) (7)⇒994 = 105 + 7n−7⇒896 = 7n⇒n = 128

It means 994 is the 128th term of AP.

Therefore, there are 128 terms in AP.

Hence, 128 three digit numbers are divisible by 7.

Answer 2

Answer:

128 digits

Step-by-step explanation:



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Questions & Answers

CBSE

Mathematics

Grade 10

Arithmetic Progression



Question

Answers

Related Questions

How many three digit numbers are divisible by 7.

A.128

B.64

C.124

D.None of these.



Answer

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Hint:Here, first, we have to find the lowest and highest 3 digit numbers which are divisible by 7, that we will get as 105 and 994. Then, we have to find the number of terms between 105 and 994 which are divisible by 7 using the formula of AP, where an=a1+(n−1)dan=a1+(n−1)d, we know the first term, last term and the common difference. We have to find the value of nn.

Complete step-by-step answer:

First consider the smallest 3 digit number 100. We have to check whether it is divisible by 7 or not.

Now, dividing 100 by 7 we get,

1007=14271007=1427, where 2 is the remainder,

Therefore 100 is not divisible by 7.

Similarly check for 101. i.e. by dividing 101 by 7 we get:

101

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