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

Solution:

The given series can be written as 

2 x 4 + 4 x 6 + 6 x 8 + .... + n terms = [(2 x 1) x (2 x 1 + 2)] + [(2 x 2) x (2 x 2 + 2)] + [(2 x 3) x (2 x 3 + 2)] + .... + n terms

By observing the pattern of the above series, its nᵗʰ term would be:

aₙ = 2n x (2n + 2)

= 4n² + 4n

a₂₀ = 4 (20)² + 4 (20)

= 4 (400) + 80

= 1680

Thus, the 20^th term of the series is 1680

NCERT Solutions Class 11 Maths Chapter 9 Exercise ME Question 22

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

Summary:

The 20ᵗʰ term of the series 2 x 4 + 4 x 6 + 6 x 8 + .... + n terms is 1680