Sum

How many two-digit numbers are divisible by 5?

Activity :- Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.

Here, d = 5, therefore this sequence is an A.P.

Here, a = 10, d = 5, t_{n} = 95, n = ?

t_{n} = a + (n − 1) `square`

`square` = 10 + (n – 1) × 5

`square` = (n – 1) × 5

`square` = (n – 1)

Therefore n = `square`

There are `square` two-digit numbers divisible by 5

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#### Solution

Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.

Here, d = 5, therefore this sequence is an A.P.

Here, a = 10, d = 5, t_{n} = 95, n = ?

t_{n} = a + (n − 1) **d**

∴ **95** = 10 + (n – 1) × 5

∴ 95 – 10 = (n – 1) × 5

∴ **85** = (n – 1) × 5

∴ `85/5` = (n – 1)

∴ **17** = (n – 1)

∴ n = 17 + 1

Therefore n = **18**

There are **18** two-digit numbers divisible by 5

Concept: General Term of an Arithmetic Progression

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