Question-21504

Question Number 21504 by mondodotto@gmail.com last updated on 25/Sep/17

Answered by $@ty@m last updated on 26/Sep/17

A T Q

S_{n} = (- 1) + 1 + 3 + 5 + \dots \dots + (2 n - 3)

(i) S_{50} = \frac{50}{2} {(- 1) + (2 \times 50 - 3)}

= 25 (- 1 + 97)

= 25 \times 96

= 2400

(i i) S_{n} = 624

\frac{n}{2} {2 a + (n - 1) d} = 624

\frac{n}{2} {- 2 + (n - 1) \times 2} = 624

n (- 1 + n - 1) = 624

n (n - 2) = 624

n^{2} - 2 n - 624 = 0

n = \frac{2 \pm \sqrt{4 + 2496}}{2}

n = \frac{2 \pm 50}{2}

n = 26, - 24

n = 26 {∵ n \in N}

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