How many three digit numbers are there which leave a remainder 2 on division on by 7
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Answer:
129
Step-by-step explanation:
Let that number be 'x'.
When divided by 7, it leaves a remainder 2. Implying, x is not divisble by 7, but x - 2 is.
Say, (x - 2)/7 = y → x - 2 = 7y, where y is any integer. x = 7y + 2.
Means,
x(all) are those 3digit numbers which are 2 more than a multiple of 7.
First term a = 7(14) + 2 = 100
Last term l = 7(142) + 2 = 996
Using the identities of AP,
=> 996 = 100 + (n - 1)7
=> 129 = n
Means, there are 129 terms
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