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Question
Find the sum of numbers between 1 to 140, divisible by 4.
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Solution
The numbers between 1 to 140 divisible by 4 are
4, 8, 12, ......, 140
The above sequence is an A.P.
∴ a = 4, d = 8 – 4 = 4
Let the number of terms in the A.P. be n.
Then, tn = 140
Since tn = a + (n – 1)d,
140 = 4 + (n – 1)(4)
∴ 140 – 4 = (n – 1)(4)
∴ 136 = (n – 1)(4)
∴ `136/4` = n – 1
∴ 34 + 1 = n
∴ n = 35
Now, `S_n = n/2 [2a + (n - 1)d]`
∴ `S_35 = 35/2 [2 xx 4 + (35 - 1)4]`
= `35/2 [8 + (34)4]`
= `35/2 [8 + 136]`
= `35/2 xx 144`
= 35 × 72
S35 = 2520
∴ The sum of numbers between 1 to 140, which are divisible by 4 is 2520.
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