# Find the 20th term of the series 2 × 4 + 4 × 6 + 6 × 8 + ... + n terms.

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive quiz on inequalities involving AM and GM45 mins
Check Your progress Part 2| Interactive Quiz: Sequence & Series47 mins
Sequence & Series (Lecture 1)56 mins
Sequence & Series (Lecture 5)42 mins
Sequence & Series (Lecture 7)37 mins
Quick Recap lecture of Sequence & Series56 mins
General Term of Miscellaneous progression46 mins
Improve your understanding of AP & GP27 mins
Geometric Progression58 mins
Sequence & Series (Lecture 4)FREE Class
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

If , then Sn is equal to

RD Sharma - Mathematics

If , find the value of .

RS Aggarwal - Mathematics

If, prove that,

.

RS Aggarwal - Mathematics