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Standard XII

Mathematics

Arithmetic Mean

If the sum of...

Question

If the sum of $n$ terms of an A.P. is given by $S_{n} = 3 n^{2} - 4 n,$ then its $50^{t h}$ term is

293

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353

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391

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412

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Solution

The correct option is A $293$
Let $T_{n}$ be the $n^{t h}$ term of A.P.
Then, $T_{n} = S_{n} - S_{n - 1}$
$= 3 n^{2} - 4 n - [3 (n - 1)^{2} - 4 (n - 1)] = 6 n - 7$

Hence, $T_{50} = 6 \times 50 - 7 = 293$

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Arithmetic Mean

Standard XII Mathematics

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If the sum of n terms of an A.P. is given by Sn=3n2−4n, then its 50th term is

The correct option is A 293Let Tn be the nth term of A.P. Then, Tn=Sn−Sn−1 =3n2−4n−[3(n−1)2−4(n−1)]=6n−7 Hence, T50=6×50−7=293

If the sum of $n$ terms of an A.P. is given by $S_{n} = 3 n^{2} - 4 n,$ then its $50^{t h}$ term is

The correct option is A $293$
Let $T_{n}$ be the $n^{t h}$ term of A.P.
Then, $T_{n} = S_{n} - S_{n - 1}$
$= 3 n^{2} - 4 n - [3 (n - 1)^{2} - 4 (n - 1)] = 6 n - 7$

Hence, $T_{50} = 6 \times 50 - 7 = 293$