How many integers between 1000 and 9999 inclusive are divisi

How many integers between 1000 and 9999 (inclusive) are divisible by 9?

Solution

NUMBER OF INTEGERS DIVISIBLE BY 9 BETWEEN 1000 AND 9999 [INCLUSIVE] WE FIND THE FIRST NUMBER AS 1008…..AND THE LAST NUMBER IS 9999.. SO THE NUMBERS ARE ….. 1008 , 1017 , 1026 , ………….9999… WHICH FORM AN ARITHMETIC SEQUENCE WITH FIRST TERM = A = 1008 ……………..N TH. TERM = T [ N ]= 9999…. COMMON DIFFERENCE = D = 9 …CONSTANT FORMULA FOR N TH. TERM IN ARITHMETIC SEQUENCE IS … T [N ] = A + [ N-1 ] D 9999 = 1008 + [N-1] * 9 N = 1000 SO THERE ARE 1000 NUMBERS DIVISIBLE BY 9 BETWEEN 1000 & 9999 [ INCLUSIVE ]