How many two-digit natural numbers are divisible by 7?

Answer:

The 2-digit number divisible by 7 is 14, 21, 28, 35……98

The first 2-digit number which is divisible by 7 is 14

The last 2-digit number which is divisible by 7 is 98

The list of 2-digit numbers divisible by 7 are

14, 21, 28, 35……98 which forms an A.P

Consider a formula

T(n) = a + (n – 1)d

Where

a = 14

d = 7

T(n) = 98

98 = 14 + (n – 1)7

84 = 7n – 7

7n = 91

n = 13

∴ There are 13 two – digits number which are divisible by 7.

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