how many three figit natural number are divisible by 5. also find the sum of all the numbers
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How many three digit numbers are divisible by 5?
A.P=100,105,110,………..,995
Therefore,a=100
d=5
a+(n-1)d=995
100+(n-1)(5)=995
(n-1)(5)=895
(n-1)=179
n=180
Therefore ,there are 180 three digit numbers which are divisible by 5
Assuming we are restricting ourselves to positive integers (if we included negative integers, the sum would trivially be 0), the smallest such number is 100. The largest is 995.
100+105+110+...+990+995100+105+110+...+990+995
=5(20+21+22+...+198+199)=5(20+21+22+...+198+199)
=5((199)(200)2−(19)(20)2)=5((199)(200)2−(19)(20)2)
=5(19900−190)=5(19900−190)
=5(19710)=5(19710)
=98550
A.P=100,105,110,………..,995
Therefore,a=100
d=5
a+(n-1)d=995
100+(n-1)(5)=995
(n-1)(5)=895
(n-1)=179
n=180
Therefore ,there are 180 three digit numbers which are divisible by 5
Assuming we are restricting ourselves to positive integers (if we included negative integers, the sum would trivially be 0), the smallest such number is 100. The largest is 995.
100+105+110+...+990+995100+105+110+...+990+995
=5(20+21+22+...+198+199)=5(20+21+22+...+198+199)
=5((199)(200)2−(19)(20)2)=5((199)(200)2−(19)(20)2)
=5(19900−190)=5(19900−190)
=5(19710)=5(19710)
=98550
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