Q. 34.1( 43 Votes )

# Find the sum of all even numbers from 1 to 350.

Answer :

List of even natural number between 1 to 350 is

2,4,6,…….348

Where first term a = 2

Second term t_{1} = 4

Third term t_{2} = 6

Thus, common difference d = t_{2} – t_{1} = 6 – 4 = 2

t_{n} = 348 (As we have to find the sum of even numbers between 1 and 350 therefore excluding 350 )

Now, By using n^{th} term of an A.P. formula

t_{n} = a + (n – 1)d

where n = no. of terms

a = first term

d = common difference

t_{n} = n^{th} terms

we can find value of “n” by substituting all the value in formula we get,

⇒ 348 = 2 + (n – 1) × 2

⇒ 348 – 2 = 2(n – 1)

⇒ 346 = 2(n – 1)

⇒ n = 173 + 1 = 174

Now, By using sum of n^{th} term of an A.P. we will find it’s sum

Where, n = no. of terms

a = first term

d = common difference

S_{n} = sum of n terms

Thus, Substituting given value in formula we can find the value of S_{n}

Thus, S_{174} = 30,450

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