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How many $4$-digit numbers are divisible by $7$?
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(b) $4$-digit numbers, divisible by $7$ are $1001, 1008, 1015, \text{......}, 9996$ (
frac{1}{2} Mark)
It is an AP with $a = 1001, d = 7, a_n = 9996$ (1 Mark)
$9996 = 1001 + (n - 1)(7)$ (
frac{1}{2} Mark)
$\Rightarrow (n-1)7 = 8995 \Rightarrow n-1 = 1285 \Rightarrow n = 1286$ (
frac{1}{2} Mark)
(b) $4$-digit numbers, divisible by $7$ are $1001, 1008, 1015, \text{......}, 9996$ (
frac{1}{2} Mark)
It is an AP with $a = 1001, d = 7, a_n = 9996$ (1 Mark)
$9996 = 1001 + (n - 1)(7)$ (
frac{1}{2} Mark)
$\Rightarrow (n-1)7 = 8995 \Rightarrow n-1 = 1285 \Rightarrow n = 1286$ (
frac{1}{2} Mark)