Question

How many three digit numbers are divisible by 7?

Answer 1

Answer:

The three digit numbers which are divisible by 7 are 128.

Step-by-step explanation:

Three digit numbers which are  divisible by 7 are 105,112,119,… ,994

First term , a = 105, Common difference ,d  = 112 - 105 = 7 , an = 994

an = a + (n -1)d

994 = 105 + (n - 1) × 7

994 = 105 + 7n - 7

994 = 105 - 7 + 7n

994 = 98 + 7n

994 - 98 = 7n

896 = 7n

n = 896/7

n = 128

Hence, the three digit numbers which are divisible by 7 are 128.

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Answer 2

Answer : 128 numbers

Step by step explanation :

To find : n ( number of terms which are divisible by 7).

So the series would be :

105, 112, 119... 994

Here,

a = 105 ( First term )

L = 994 ( Last term )

d = 7 ( common difference )

As per the formula

994 = 105 + (n - 1) 7

= 105 + 7n - 7

994 = 98 + 7n

994 - 98 = 7n

896/7 = n

n= 128

Thus, 128 three digit numbers are divisible by 7.

Answer: 128 numbers.