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

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

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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