Find the 20th term and the sum of 20 terms of the series: `2xx4+4xx6+6xx8+ dot`

Answer

N/a

Explanation

Given series `= 2 xx 4 + 4 xx 6 + 6 xx 8 + … + ` to n terms
20th term of this series = (20th term of 2, 4, 6, ...) `xx` (20th term of 4, 6, 8, …)
`rArr` `a_(20) = [2 + (20 - 1)2] xx [4 + (20 - 1)2]`
`= [2 + (19 xx 2)] xx [4 + (19 xx 2)]`
`= [2 + 38] xx [4 + 38]`
`= 40 xx 42 = 1680`