Theory of Intelligence
11TH•Mathematics•Sequences And Series•Question 12

Overview

How many numbers of three digits are divisible by 7?

Three-digit numbers divisible by 7 form an A.P.

First three-digit multiple of 7: ( 105 ) (( 7 \times 15 ))

Last three-digit multiple of 7: ( 994 ) (( 7 \times 142 ))

[ a = 105,\ d = 7,\ a_n = 994 ]

[ 105 + (n-1)7 = 994 ] [ (n-1)7 = 889 ] [ n-1 = 127 ] [ n = 128 ]

Answer: 128

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