How many three-digit numbers are divisible by 7?
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Answered by
1
128 three digit number divisible by 7
Answered by
1
Step-by-step explanation:
Three Numbers which are divisible by 7 are
105,112,119,.....994
which forms an A.P
first term of this A.P a
1
=105
second term of this A.P is a
2
=112
common difference of this A.P is
d=a
2
−a1=112−105=7
nth term of this A.P is given by
a
n
=a
1
+(n−1)d
⟹a
n
=105+(n−1)7
⟹a
n
=105+7n−7
⟹a
n
=98+7n...….eq(1)
for finding number of terms(n) in this A.P put last term a
n
=994 in eq(1)
⟹994=98+7n
⟹7n=994−98
⟹7n=896
⟹n= 896÷7
⟹n=128
hence, their are 128 three digit numbers which are divisible by 7
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