Question

find the sum of first 30 even number​

Answer 1

How to Find the Sum of First 30 Even Numbers?

The below workout with step by step calculation shows how to find what is the sum of first 30 even numbers by applying arithmetic progression. It's one of the easiest methods to quickly find the sum of given number series.

step 1 Address the formula, input parameters & values.

Input parameters & values:

The number series 2, 4, 6, 8, 10, 12, .  .  .  .  , 60.

The first term a = 2

The common difference d = 2

Total number of terms n = 30

step 2 apply the input parameter values in the AP formula

Sum = n/2 x (a + Tn)

= 30/2 x (2 + 60)

= (30 x 62)/ 2

= 1860/2

2 + 4 + 6 + 8 + 10 + 12 + .  .  .  .   + 60 = 930

Therefore, 930 is the sum of first 30 even numbers.

Answer 2

SOLUTION

TO DETERMINE

The sum of first 30 even number

CONCEPT TO BE IMPLEMENTED

Sum of first n terms of an arithmetic progression

$\displaystyle \sf = \frac{n}{2} \bigg[2a + (n - 1)d \bigg]$

Where First term = a

Common Difference = d

EVALUATION

First 30 even numbers are

2 , 4 , 6 , 8 , . . .

It is an arithmetic progression

First term = a = 2

Common Difference = d = 4 - 2 = 2

Number of terms = n = 30

Hence the required sum

Sum of first n terms of an arithmetic progression

$\displaystyle \sf = \frac{n}{2} \bigg[2a + (n - 1)d \bigg]$

$\displaystyle \sf = \frac{30}{2} \times \bigg[(2 \times 2) + (30 - 1) \times 2 \bigg]$

$\displaystyle \sf = 15 \times \bigg[4 + (29 \times 2) \bigg]$

$\displaystyle \sf = 15 \times \bigg[4 +58 \bigg]$

$\displaystyle \sf = 15 \times 62$

$\displaystyle \sf =930$

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