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प्रश्न
Find the sum of numbers between 1 to 140, divisible by 4
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उत्तर
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, Sn = `"n"/2 [2"a" + ("n" - 1)"d"]`
∴ S35 = `35/2 [2xx4+(35-1)4]`
= `35/2[8+(34)4]`
= `35/2[8+136]`
= `35/2xx144`
= 35 × 72
S35 = 2520
∴ The sum of numbers between 1 to 140, which are divisible by 4 is 2520.
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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`
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