Question

How many number between 11 and 111 are multiple of 3?

Answer 1

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :}}}}}{\star}$

Given :-

A. P :- 12, 15, 18, ...........108

First term(a) = 12

Common difference(d) = 15 - 12 = 3

Last term(an) = 108

To Find :-

Value of n

Solution :-

We know that,

$\LARGE{\underline{\boxed{\red{\sf{a_{n} = a + (n - 1)d}}}}}$

______________[Put Values]

108 = 12 + (n - 1)3

➡ ️108 = 12 + 3n - 3

➡ 108 = 9 + 3n

➡ 108 - 9 = 3n

➡ 99 = 3n

➡ n = 99/3

➡ n = 33

$\large{\underline{\boxed{\blue{\sf{n \: = \: 33}}}}}$

Answer 2

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Let a and d be the first term and common difference of the following A.P

The A.P would be:

12,15,18,...................,111

Here,

• First term,a = 12

• Common Difference,d = 3

• Last term,l = 111

Let there be n no.of terms between 11 and 111

Using the Formula,

$\huge{\green{\underline{\boxed{\sf{l= a + (n - 1)d}}}}}$

Substituting the values,we get:

111 = 12 + (n - 1)3

→ 111 = 3n + 12 - 3

→ 111 = 3n + 9

→3n = 111 - 9

→ 3n = 102

→n = 102/3

→n = 34

Thus,there are 34 multiples of 3 between 11 and 111