Question

Question 22 Find the 20th term of the series 2 × 4 + 4 × 6 + 6 × 8 + … + n terms.

Class X1 - Maths -Sequences and Series Page 200

Answer 1

Here series is 2 × 4 + 4 × 6 + 6 × 8 + .... + n terms

we will break the series into two parts are 2, 4 , 6, ...... and 4 , 6, 8 ....... and then find the nth term of each part separately for finding nth term of the given series .

Tₙ = { nth term of 2, 4, 6 ...}{nth term of 4, 6, 8,...}
use formula,
nth term of AP = a + ( n - 1)d
Tₙ = { 2 + ( n - 1) × 2 }{ 4 + ( n - 1) × 2 }
= { 2 + 2n - 2}{ 4 + 2n - 2 }
= 2n (2n + 2)
= 4n(n + 1)
hence, Tₙ = 4n(n + 1)
now,
T₂₀ = 4 × 20 × (20 + 1)
= 80 × 21
= 1680

Answer 2

Answer:

The given series is 2×4+4×6+6×8+....+n terms

nth term=a

n

=2n×(2n+2)=4n

2

+4n

a

20

=4(20)

2

+4(20)=1600+80=1680

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