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Find the 50th term of the series 2+3+6+1...

Find the 50th term of the series `2+3+6+11+18+…`.

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Let `S_(n)=2+3+6+11+18+...+T_(n-1)+T_(n)`.
Again `S_(n)=2+3+6+11+...+T_(n-1)+T_(n)`.
On substracting, we get
`0=2+[1+3+5+7+... "to"(n-1)"terms"]-T_(n)`
`rArr T_(n)=2+[1+3+5+7+... "to"(n-1)"terms"]`
`=2+((n-1))/(2)*[2xx1+(n-2)xx2]=(n-1)^(2)+2.`
`rArr T_(50)={(50-1)^(2)+2}={(49)^(2)+2}=(2401+2)=2403.`
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