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# Find Out the Sum of All Natural Numbers Between 1 and 145 Which Are Divisible by 4. - Algebra

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Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.

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#### Solution

The numbers divisible by 4 between 1 and 145 are
4, 8, 12, 16, .........144 ; which is an A. P.
Here, a = 4, d = 4, tn = 144 we have to find n.
tn = a + (n - 1) d
∴tn = 4 + (n - 1) × 4
∴ 144 = 4n
∴ n = 36
Now, s_n = n/2[t_1+t_n]
∴ S_36 = 36/2 [4+144]
= 18 × 148 = 2664
Alternate Method
4 + 8 + 12 + ..... + 144
= 4(1 + 2 + 3 + ..... + 36)
= (4xx36xx37)/2
= 12 × 6 × 37
= 444 × 6
= 2664
This is also possible.

∴ The sum of numbers between 1 and 145 divisible by 4 is 2664.

Concept: Sum of First n Terms of an AP
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