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  • Find the sum of the first 9 terms of the series whose nth term is 2n^3 + 2n^2 +3n+9. calculate the 25th term.  Option: 1 4556, 32684</

Find the sum of the first 9 terms of the series whose nth term is 2n^3 + 2n^2 +3n+9. calculate the 25th term.

 

Option: 1

4556, 32684


Option: 2

1589,35896


Option: 3

8759,25896


Option: 4

3600,25874


Answers (1)

best_answer

To find the sum of the first 9 terms of the series with the nth term as 2n^3 + 2n^2 + 3n + 9, we can follow the same process as before. 

Adding up the terms for n = 1, 2, 3, 4, 5, 6, 7, 8, and 9:

\begin{aligned} & 2(1)^3+2(1)^2+3(1)+9=2+2+3+9=16 \\ & 2(2)^3+2(2)^2+3(2)+9=16+8+6+9=39 \\ & 2(3)^3+2(3)^2+3(3)+9=54+18+9+9=90 \\ & 2(4)^3+2(4)^2+3(4)+9=128+32+12+9=181 \\ & 2(5)^3+2(5)^2+3(5)+9=250+50+15+9=324 \\ & 2(6)^3+2(6)^2+3(6)+9=432+72+18+9=531 \\ & 2(7)^3+2(7)^2+3(7)+9=686+98+21+9=814 \\ & 2(8)^3+2(8)^2+3(8)+9=1024+128+24+9=1185 \\ & 2(9)^3+2(9)^2+3(9)+9=1458+162+27+9=1656 \end{aligned}
Summing up these terms:
16+39+90+181+324+531+814+1185+1656=4556

Therefore, the sum of the first 9 terms of the series is 4556 .
To find the 25th term, we substitute \mathrm{n}=25  into the given expression:

2(25)^3+2(25)^2+3(25)+9=2(15625)+2(625)+75+9=31250+1250+75+9=32684
Therefore, the 25th term of the series is 32684 .

Posted by

shivangi.bhatnagar

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