Question

find the value of 26+28+....+28th even number

Answer 1

Answer:

the answer is 26 mate

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Answer 2

The value of 26 + 28 + . . . + 28th even number is 656

Given :

26 + 28 + . . . + 28th even number

To find :

The value of 26 + 28 + . . . + 28th even number

Concept :

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

Solution :

Step 1 of 3 :

Find 28th even number

28th even number

= 28 × 2

= 56

Step 2 of 3 :

Find the number of terms

We have to find 26 + 28 + . . . + 28th even number

Now

The value of 26 + 28 + . . . + 28th even number is

= 26 + 28 + . . . + 56

This is an arithmetic progression

First term = a

Common Difference = d = 28 - 26 = 2

Let 56 is nth term of the AP

Then

a + ( n - 1 )d = 56

⇒ 26 + 2(n - 1) = 56

⇒ 2(n - 1) = 30

⇒ n - 1 = 15

⇒ n = 16

There are 16 terms in the AP

Step 3 of 3 :

Find the sum

The required sum

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

$\displaystyle \sf = \frac{16}{2} \bigg[(2 \times 26) + (16 - 1) \times 2 \bigg]$

$\displaystyle \sf = 8 \times \bigg[52 + 30 \bigg]$

$\displaystyle \sf = 8 \times 82$

$\displaystyle \sf = 656$

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