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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 seque - Algebra

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Sum

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, tn = 136, Sn = ?

tn = a + (n – 1)d

`square` = 4 + (n – 1) × 4

`square` = (n – 1) × 4

n = `square`

Now,

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

Sn = 17 × `square`

Sn = `square`

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

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Solution

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, tn = 136, Sn = ?

tn = a + (n – 1)d

∴ 136 = 4 + (n – 1) × 4

∴ 136 – 4 = (n – 1) × 4

∴ 132 = (n – 1) × 4

∴ `132/4` = n – 1

∴ 33 = n – 1

∴ n = 34

Now,

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

∴ Sn = `34/2 (4 + 136)`

∴ Sn = 17 × 140

∴ Sn2380

Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is 2380.

Concept: Sum of First n Terms of an AP
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