Question

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.

Answer 1

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) \[\boxed{\text{d}}\]

 ∴ \[\boxed{95}\] = 10 + (n – 1) × 5

∴ 95 – 10 = (n – 1) × 5

∴ \[\boxed{85}\] = (n – 1) × 5

∴ `85/5` = (n – 1)

∴ \[\boxed{17}\] = (n – 1)

∴ n = 17 + 1

Therefore n = \[\boxed{18}\]

There are \[\boxed{18}\] two-digit numbers divisible by 5.