Question

The sum of first 20 terms of the AP: 10, 6, 2,... is​

Answer 1

Answer:

-400 is the answer

Step-by-step explanation:

hope it will help

thanks....

Answer 2

The sum of first 20 terms of the AP 10 , 6 , 2 , . . . is - 560

Given :

The arithmetic progression 10 , 6 , 2 , . . .

To find :

The sum of first 20 terms of the AP

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 :

Write down the given progression

Here the given arithmetic progression is

10 , 6 , 2 , . . .

Step 2 of 3 :

Write down first term and common difference

First term = a = 10

Common Difference = d = 6 - 10 = - 4

Step 3 of 3 :

Find the sum of first 20 terms of the AP

Number of terms = n = 20

Hence the sum of first 20 terms of the AP

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

$\displaystyle \sf = \frac{20}{2} \times \bigg[(2 \times 10) + (20 - 1) \times ( - 4) \bigg]$

$\displaystyle \sf = 10 \times \bigg[20 -( 4 \times 19) \bigg]$

$\displaystyle \sf = 10 \times \bigg[20 -76 \bigg]$

$\displaystyle \sf = 10 \times ( - 56)$

$\displaystyle \sf = - 560$

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