Find the 20

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.

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