Q. 9

# Find the 20th term and the sum of 20 terms of the series :2 × 4 + 4 × 6 + 6 × 8 + ……………..

Given: 2 × 4 + 4 × 6 + 6 × 8 + ……………..

The nth term would be from given series 2n × (2n + 2)

The general term would be from given series 2r × (2r + 2)

Thus 20th term be 2(20) {2(20) + 2} = 40 × 42 = 1680

Summation=1st term + 2nd term + …… + 20th term

= 2 × 4 + 4 × 6 + 6 × 8 + …… 40 × 42 (1)

We know

Thus

From (1) we have

Summation =

We know by property that:

∑axn + bxn - 1 + cxn - 2…….d0=a∑xn + b∑xn - 1 + c∑xn - 2…….. + d0∑1

Thus,

(2)

We know

Thus

Thus substituting in above equation in (2)

=4(10)(7)(41) + 4(10)(21)

=12320

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