Arithmetic Progressions

Seven Problems You must Know

Question: How many three digits multiples of 7 are there ?
Answer: Multiple of 7 having three digits are 105, 112, 119, ... 994
 $\Rightarrow a = 105, d = 7, T_n = 994$
 $\Rightarrow 994 = 105 + 7(n - 1)$
 $\Rightarrow n - 1 = \frac{889}{7}$
 $\Rightarrow n = 128$
 $\therefore$   There are 128 three-digit multples of 7
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