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प्रश्न
Find the sum of the first 40 positive integers divisible by 3
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उत्तर
In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,
`S_n = n/2 [2a + (n - 1)d]`
Where; a = first term for the given A.P.
d = common difference of the given A.P.
First 40 positive integers divisible by 3
n = number of terms
First 40 positive integers divisible by 3
So, we know that the first multiple of 3 is 3 and the last multiple of 3 is 120.
Also, all these terms will form an A.P. with the common difference of 3.
So here,
First term (a) = 3
Number of terms (n) = 40
Common difference (d) = 3
Now, using the formula for the sum of n terms, we get
`S_n = 40/2 [2(3) + (40 - 1)3]`
= 20[6 + (39)3]
= 20(6 + 117)
= 20(123)
= 2460
Therefore, the sum of first 40 multiples of 3 is 2460
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