Complete the following activity to find the sum of natural numbers from 1 to 140 which are divisible by 4.

Sum of numbers from 1 to 140, which are divisible by 4 =

List of natural number divisible by 4 between 1 to 140 is

4,8,12,…….136

Where first term a = 4

Second term t₁ = 8

Third term t₂ = 12

Thus, common difference d = t₂ – t₁ = 12 – 8 = 4

t_n = 136

Now, By using n^th term of an A.P. formula

t_n = a + (n – 1)d

where n = no. of terms

a = first term

d = common difference

t_n = n^th terms

we can find value of “n” by substituting all the value in formula we get,

⇒ 136 = 4 + (n – 1) × 4

⇒ 136 – 4 = 4(n – 1)

⇒ 132 = 4(n – 1)

⇒ n = 33 + 1 = 34

Now, By using sum of n^th term of an A.P. we will find it’s sum

Where, n = no. of terms

a = first term

d = common difference

S_n = sum of n terms

Thus, Substituting given value in formula we can find the value of S₃₄

⇒S₃₄ = 17 × [8 + 33×4]

⇒S₃₄ = 17 × [8 + 132]

⇒S₃₄ = 17 × 140 = 2380

Thus, S₃₄ = 2380