Question

Find the sum of natural numbers between 1 to 140, which are divisible by 4.

Activity: Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136

Here d = 4, therefore this sequence is an A.P.

a = 4, d = 4, t_n = 136, S_n = ?

t_n = a + (n – 1)d

`square` = 4 + (n – 1) × 4

`square` = (n – 1) × 4

n = `square`

Now,

S_n = `"n"/2["a" + "t"_"n"]`

S_n = 17 × `square`

S_n = `square`

Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.

Answer 1

Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136

Here d = 4, therefore this sequence is an A.P.

a = 4, d = 4, t_n = 136, S_n = ?

t_n = a + (n – 1)d

∴ \[\boxed{136}\] = 4 + (n – 1) × 4

∴ 136 – 4 = (n – 1) × 4

∴ \[\boxed{132}\] = (n – 1) × 4

∴ `132/4` = n – 1

∴ 33 = n – 1

∴ n = \[\boxed{34}\]

Now,

S_n = `"n"/2["a" + "t"_"n"]`

S_n = `34/2 (4 + 136)`

∴ S_n = 17 × \[\boxed{140}\]

∴ S_n = \[\boxed{2380}\]

Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is \[\boxed{2380}\].