Question

2+4+6+8+...sum of first 12 even positive integer is​

Answer 1

Answer:

The number series 2, 4, 6, 8, 10, 12, . . . . Therefore, the sum of first 12even positive and nteger is 156

Answer 2

2 + 4 + 6 + 8 + ... sum of first 12 even positive integer is 156

Given :

2 + 4 + 6 + 8 + ...

To find :

2 + 4 + 6 + 8 + ... sum of first 12 even positive integer

Formula :

Sum of first n terms of an arithmetic progression

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

Where First term = a

Common Difference = d

Solution :

Step 1 of 3 :

Write down the given series

Here the given series is 2 + 4 + 6 + 8 + ...

This is an arithmetic series

Step 2 of 3 :

Write down first term and common difference

First term = a = 2

Common Difference = d = 4 - 2 = 2

Step 3 of 3 :

Calculate sum of series

Number of terms = 12

∴ The required sum

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

$\displaystyle \sf = \frac{12}{2} \bigg[(2 \times 2) + (12 - 1) \times 2 \bigg]$

$\displaystyle \sf = 6 \times \bigg[4 + 22 \bigg]$

$\displaystyle \sf = 6 \times 26$

$\displaystyle \sf = 156$

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