Attempt this Sum of N terms of an arithmetic progression question of 17 January 2022

Question of The Day17-01-2022

What is the sum of all even natural numbers smaller than 301?

Answer

Correct Answer : b ) 11400

Explanation :

As we know that, natural numbers are integers starting from 1, 2, 3,......so on.

Even Numbers are numbers that gives remainder as 0 when divided by 2.

The even natural numbers are 2, 4, 6, 8,....

In the given question, the last term of the series will be 300.

The series is 2, 4, 6, 8,.........300

The series is an arithmetic progression with

First term, a₁ = 2

Common difference, d = 2

Last term, l = 300

We know that,

a_n = a₁ + (n-1)*d

To find n,

300 = 2 +(n - 1)*2

298/2 = n - 1

149 + 1 = n

n = 150

We know that,

Sum of n terms, S_n = (n/2)* [a + l]

S₁₅₀ = (150/2)*[2 + 150]

S₁₅₀ = 11400

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