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  • The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + ….. is :Option: 1 3450Option

The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + ….. is :

Option: 1

3450


Option: 2

3420


Option: 3

3520


Option: 4

3250


Answers (1)

best_answer

\mathrm{S}_{\mathrm{n}}=5+11+19+29+41+\ldots \ldots+\mathrm{T}_{\mathrm{n}}
\mathrm{S}_{\mathrm{n}}=5+11+19+29+\ldots+\mathrm{T}_{\mathrm{n}-1}+\mathrm{T}_{\mathrm{n}}
0=5+\{\underbrace{6+8+10+12+\ldots}_{(\mathrm{n}-1) \text { terms }}\}-\mathrm{T}_{\mathrm{n}}

\mathrm{T}_{\mathrm{n}}=5+\frac{(\mathrm{n}-1)}{2}[2 \cdot 6+(\mathrm{n}-2) \cdot 2]
\mathrm{T}_{\mathrm{n}}=5+(\mathrm{n}-1)(\mathrm{n}+4)=5+\mathrm{n}^2+3 \mathrm{n}-4=\mathrm{n}^2+3 \mathrm{n}+1

\text { Now } \mathrm{S}_{20}=\sum_{\mathrm{n}=1}^{20} \mathrm{~T}_{\mathrm{n}}=\sum_{\mathrm{n}=1}^{20} \mathrm{n}^2+3 \mathrm{n}+1

\mathrm{~S}_{20}=\frac{20.21 .41}{6}+\frac{3.20 .21}{2}+20
\mathrm{~S}_{20}=2870+630+20
\mathrm{~S}_{20}=3520

Posted by

Suraj Bhandari

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