Question

given that (12+22+32+.......102)=385 ,then the value of (22+42+62+.......+202) is

Answer 1

The answer is 750 ... please reply.

Answer 2

Answer:

The value of  (22+42+62+.......+202) is 1120 .

Step-by-step explanation:

Airthmetic equation is given by

$a_{n} = a_{1}+(n-1)d$

$S_{n} = \frac{n}{2}[a_{1}+a_{n}]$

$d = a_{2}-a_{1}$

Where $a_{n}$ is the nth term , $a_{1}$ is the first term and d is the common difference .

As given the equation

12 + 22 + 32 + .......102 = 385

Now consider the series  22 + 42 + 62 + ....... + 202 .

$a_{1}=22$

$a_{2} = 42$

$d =42-22$

d = 20

$a_{n}=202$

$202=22+(n-1)20$

202 = 22 + 20n - 20

202 = 2 + 20n

202 - 2 = 20n

200 = 20n

$n = \frac{200}{20}$

n = 10

Thus the series 22 + 42 + 62 + ....... + 202 contains 10 terms .

$S_{10} = \frac{10}{2}[22+202]$

$S_{10} = \frac{10}{2}\times [224]$

$S_{10} =5\times [224]$

$S_{10} =1120$

Therefore the value of  (22+42+62+.......+202) is 1120 .