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Summation by Sigma Method

Let nth ter...

Question

Let $n^{t h}$ term of sequence $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, . . . . .$ is given by $t_{n}$ , then ?

t_{100} = 14

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t_{200} = 20

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t_{300} = 24

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t_{400} = 28

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Solution

The correct option is A $t_{100} = 14$
$n o . o f t e r m s w i t h s a m e v a l u e s a r e i n A P (l e t^{'} s c a l l t h e m a s a g r o u p) 100 = (\frac{n (n + 1)}{2}) n (n + 1) = 200 f o r n = 14 n (n + 1) = 210 > 200 h e n c e a l l t e r m s w i t h v a l u e s 14, w i l l c o v e r g r o u p i n c l u d i n g 100 t h t e r m$

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