Q. 9

Find the 20th term and the sum of 20 terms of the series :

2 × 4 + 4 × 6 + 6 × 8 + ……………..

Answer :

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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