N th term of the series 2-4-7-11- will beA- n2-n-1-2B- n2-n-2C- n2-n-2-2D- n2-2 n-2-2

The correct option is C Let S = 2 + 4 + 7 + 11 + 16 + ...........+ T_n nbsp; nbsp; nbsp; S = 2 + 4 + 7 + 11 + 16 + ...........T_n 1 + T_n Subtracting ...

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Standard XI

Mathematics

Sigma n

n th term of ...

Question

$n^{t h}$ term of the series 2 + 4 + 7 + 11 + ...... will be

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Solution

The correct option is C

Let S = 2 + 4 + 7 + 11 + 16 + ...........+ $T_{n}$

S = 2 + 4 + 7 + 11 + 16 + ........... $T_{n - 1}$ + $T_{n}$

Subtracting, we get

0 = 2 + {2 + 3 + 4 +..........+( $T_{n} - T_{n - 1}$ )} - $T_{n}$

⇒ $T_{n}$ = 1 + (1 + 2 + 3 + 4 + .........upto n terms)

⇒ 1 + $\frac{1}{2}$ n(n+1) = $\frac{2 + n^{2} + n}{2}$ = $\frac{n^{2} + n + 2}{2}$

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nth term of the series 2 + 4 + 7 + 11 + ...... will be

The correct option is C Let S = 2 + 4 + 7 + 11 + 16 + ...........+ Tn S = 2 + 4 + 7 + 11 + 16 + ...........Tn−1 + Tn Subtracting, we get 0 = 2 + {2 + 3 + 4 +..........+(Tn−Tn−1)} - Tn ⇒ Tn = 1 + (1 + 2 + 3 + 4 + .........upto n terms) ⇒ 1 + 12n(n+1) = 2+n2+n2 = n2+n+22

$n^{t h}$ term of the series 2 + 4 + 7 + 11 + ...... will be