the set of all positive integers which leaves remainder 5 when divided by 7 are
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129
Step-by-step explanation:
Least 3-digit number=100
Greatest 3-digit number=999
Least 3-digit number when divided by 5 leaves remainder as 7=103
Greatest 3-digit number when divided by 5 leaves remainder as 7=999
So, an A.P. is formed in this way:
103, 110, ......., 999
where d =7
Now,
aₙ=999
a=103
We know,
aₙ=a+(n-1)d
⇒999=103+(n-1)7
⇒896=7(n-1)
⇒n-1=128
⇒n=129
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