Question

what is the sum of all even numbers from 1 to 701

Answer 1

From the above details, we have to find the total of all even numbers exactly from 1 to 701.  

If we calculate the even numbers manually it will takes more time duration.  

The calculation will goes like 2+ 4+ 6+ 8+ 10+ .............+ 696+ 698 + 700.

We can simplified the process by 700/2=350. The next step is 350*351=122850.

Answer 2

The sum of all even numbers from 1 to 701 is 122850.

Given: even numbers from 1 to 701

To find: Sum of all even numbers from 1 to 701

Formula used:

nth term of an A.P, $a_n$ = a + (n - 1)d

Sum of nth terms ,$S_n = \frac{n}{2} [a + l]$

Here,a = first term, a_n = nth term, d = common Difference, l = last term ($a_n$ = l)

Solution:

Step 1: Write even numbers from 1 to 701:

2, 4, 6, 8, 10, 12…………..698, 700.

Here, a = 2 , d = 2 , $a_n$ = 700

Step2: Find the number of terms, n:

By using the formula ,$a_n$ = a + (n - 1)d

700 = 2 + (n - 1) × 2

700 = 2 + 2n - 2

700 = 2n

n = $\frac{700}{2}$

n = 350

Number of terms,n = 350

Step3: Find the sum of even numbers from 1 to 701:

By using the formula, Sum of nth terms, $S_n$ = $\frac{n}{2} [a + l]$

$S_n$ = $\frac{350}{2} [2 + 700]$

[n = 350, l = 700]

$S_n$ = 175 × 702

$S_n$ = 122850

Hence, the sum of all even numbers from 1 to 701 is 122850.

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