The 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
tn = 136
Now, by using nth term of an A.P. formula
tn = a + (n – 1) d
where n = no. of terms
a = first term
d = common difference
tn = nth 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 – 1 = 132/4 = 33
⇒ n = 33 + 1 = 34
Now, by using sum of nth term of an A.P. we will find its sum
Where, n = no. of terms
a = first term
d = common difference
Sn = 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