Complete the following activity to find the sum of natural number between 1 and 140. Which are divisible by 4
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Answer:
These numbers from an A.P. with a = 4, d = 4
Let, 140 be the nth term of A.P.
∴ tn = 140
tn = a + (n – 1) d
∴ 140 = 4 + (n – 1) 4
∴ 140 = 4 + 4n – 4
∴ 140 = 4n
∴ n = 140/4
∴ n = 35
∴ 140 is 35 term of A.P.
Now, We have to find sum of 35 terms i.e. S35,
Sn = n/2[2a + (n – 1)d]
∴ S35 = 35/2 [2 (4) + (35 – 1) 4]
∴ S35 = 35/2[8 + 34 (4)]
∴ S35 = 35/2 [8 + 136)
∴ S35 = 35/2 [144]
∴ S35 = 2520
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