How many numbers are there between 200 and 500, which leave remainder 7 when divided by 9 - Maths - Sequences and Series

Question

How many numbers are there between 200 and 500, which leave
remainder 7 when divided by 9

Shruti Tyagi · Accepted Answer

Dear student,

The numbers between 200 and 500 which leaves remainder 7 when divided by 9 are as follows205, 214, 223,
493which is an AP with common difference 9using an=a+n-1d⇒493=205+n-1×9⇒493-205=9n-1⇒288=9(n-1)⇒2889=n-1⇒32=n-1⇒32+1=n⇒n=33thus there are 33 such numbers that are between 200 and 500 which leaves remainder 7 when divided by 9

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How many numbers are there between 200 and 500, which leave remainder 7 when divided by 9.