Question

which number is between 101 and 9784​

Answer 1

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The list of numbers between 101 and 999 that are divisible by 2 and 5 are:

110,120,130,...990

The numbers are in A.P, with first term, a=110, common difference, d=10

Last term, a

n

=990

We know that, a

n

=a+(n−1)d

990=110+(n−1)10

⇒990–110=10n–10

⇒880+10=10n

⇒890=10n

⇒n=89

Therefore, the number of terms between 101 and 999 that are divisible by 2 and 5 are 89.

Answer 2

The list of numbers between 101 and 999 that are divisible by 2 and 5 are:

110,120,130,...990

The numbers are in A.P, with first term, a=110, common difference, d=10

Last term, a

n

=990

We know that, a

n

=a+(n−1)d

990=110+(n−1)10

⇒990–110=10n–10

⇒880+10=10n

⇒890=10n

⇒n=89

Therefore, the number of terms between 101 and 999 that are divisible by 2 and 5 are 89.