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Find the sum of numbers between 1 to 140, divisible by 4 - Algebra

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Sum

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, ......, 136

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 = 136

Since tn = a + (n – 1)d,

136 = 4 + (n – 1)(4)

∴ 136 = 4 + 4n – 4

∴ 136 = 4n

∴ n = `136/4`  = 34

Now, Sn = `"n"/2 ("t"_1 + "t"_"n")`

∴ S34 = `34/2 (4 + 136)`

= 17(140)

= 2380

∴ The sum of numbers between 1 to 140, which are divisible by 4 is 2380.

Concept: Sum of First n Terms of an AP
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