Question

how many numbers upto 100 are divisible by 7

Answer 1

Answer:

The number of numbers up to 100 are divisible by 7 = 14

Step-by-step explanation:

To find,

The number of multiples of 7 till 100.

Solution:

Recall the concept:

The number of terms of an AP is given by

n = $\frac{a_n - a_1}{d} +1$, where aₙ is the last term, a₁ is the first term, and 'd' is the common difference of the AP

The first number divisible by 7 from 1 to 100 = 7

To find the last number divisible by 7 from 1 to 100

We have,

100 = 14×7 +2

100 -2 = 14×7

98 = 14×7

The last number divisible by 7 from 1 to 100 = 98

The set of numbers divisible by 7 from 1 to 100 are

7,14,21,..............98

This forms an AP with first term = 7 and common difference = d = 7

Required to find the number of terms of this AP

We have the number of terms of the AP,

n = $\frac{a_n - a_1}{d} +1$,

Substituting the values of

aₙ = 98, a₁ = 7 and d = 7

n = $\frac{98 - 7}{7} +1$

= $\frac{91}{7} +1$

= 13 +1

= 14

The number of terms of the AP = 14

∴ The number of numbers up to 100 are divisible by 7 = 14

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