Arithmetic Progression: How many 3 digit no.s are divisible by 7?
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Answer:
128
Step-by-step explanation:
The first 3-digit number which is divisible by 7 is 105
The last 3-digit number which is divisible by 7 is 994
The list of 3-digit numbers divisible by 7 are 105, 112, 119,…..994 which forms an A.P
Consider a formula ,
T(n) = a + (n – 1)d
Where
a = 105
d = 7
T(n) = 994
994 = 105 + (n – 1)7
889 = 7n – 7
7n = 896
n = 128
∴ There are 128 3-digits number which are divisible by 7.
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