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How many number between 1000 and 5000 are exactly divisible by 225?1). 162). 183). 194). 12 |
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Answer» First multiple of 225 after 1000 is 1125 = 225 × 5 And last multiple of 225 before 5000 is 4950 = 225 × 22 As numbers are DIVISIBLE by 225, they will form an arithmetic PROGRESSION with first TERM 1125 and last term 4950, with common DIFFERENCE 225. ∴ 1st term of this arithmetic progression is 1125 & last term of this arithmetic progression is 4950. ∴ nth term of A.P. = 1st term + (n – 1)d Where n is number of terms & d is common difference ⇒ 4950 = 1125 + (n – 1) × 225 ⇒ 3825 = (n – 1) × 225 ⇒ n – 1 = 17 ∴ n = 18 Thus there are total 18 numbers in between 1000 & 5000 which are divisible by 225. |
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