The 20th term of the series 2 x 4 + 4 x 6 + 6 x 8 ....... is

Question

from maths .What is the 20th term?

The 20th term of the series 2 x 4 + 4 x 6 + 6 x 8 ....... is

Answer 1

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

 

Answer 2

The nth term is t(n) = 2n x 2(n+1).

t(20) = 2(20) x 2(21) = 1680