Question

Solve that sum if you Can..Good Explanation will be mark as brainliest...

Answer 1

hey there,

There is more than on way to do this.

The most powerful method is to find the pattern, and express it as a function

i.e. the first term is (2x1)*(2x2)

the 2nd term is (2x2)*(2x3)

so the pattern is (2xn)*(2x(n+1))

and the 20th term is (2x20)*(2x21)

......OR......

A more intuitive approach would be to see that the first part of the series looks like the even numbers, and the second part also looks like the even numbers but shifted by 2.

So the 20th even number is 40, and the 20th term is 40x42

hope this helps!

Answer 2

Hey mate..

Here's your answer...

Answer :

The given series is in the form of multiplication of two different APs.

So, the nth term of given series is equal to the multiplication of their nth term.

The First AP is given as follows: -

2, 4, 6…

where, first term(a) = 2

common difference(d) = 4 - 2 = 2

∴

nth term = a + (n - 1)d

= 2 + (n - 1)2

= 2 + 2n - 2

= 2n

The Second AP is given as follows: -

4, 6, 8…

where, first term(a) = 4

common difference(d) = 6 - 4 = 2

∴

nth term = a + (n - 1)d

= 4 + (n - 1)2

= 4 + 2n - 2

= 2n + 2

Now,

an = [nth term of 2, 4, 6…] × [nth term of 4, 6, 8…]

= (2n) × (2n + 2)

= 4n2 + 4n

Thus, the nth term of series 2 × 4 + 4 × 6 + 6 × 8 + ... is

an = 4n2 + 4n

∴ a20 = 4 × (20)2 + 4 × 20 = 1600 + 80 = 1680

Hence, 20th term of series is 1680.

Hope this helps u dude

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