2 + 7 + 12 + ... + x = 270 Find: x = ?


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Question Number 199602 by hardmath last updated on 05/Nov/23

$2 + 7 + 12 + . . . + x = 270$ $Find : x = ?$
	Answered by Rasheed.Sindhi last updated on 06/Nov/23

	$a = 2, d = 5$ $S_{n} = \frac{n}{2} (2 a + (n - 1) d)$ $S_{n} = \frac{n}{2} (2 (2) + (n - 1) (5)) = 270$ $4 n + 5 n^{2} - 5 n = 540$ $5 n^{2} - n - 540 = 0$ $\Rightarrow n \notin N \Rightarrow T h e q u e s t i o n i s d e f e c t i v e .$
	Answered by emilagazade last updated on 05/Nov/23

	$\frac{x + 2}{2} (\frac{x - 2}{5} + 1) = 270$ $(x + 2) (x + 3) = 2700$ $x^{2} + 5 x - 2694 = 0$ $x {i s n}^{'} t n a t u r a l b u t i t m u s t . s o m e t h i n g w r o n g .$ $s u m s h o u l d b e 245 o r 297 b u t 270 {d o e s}^{'} t w o r k$
	Answered by Frix last updated on 05/Nov/23

	$S_{n} = \underset{k = 0}{\sum^{n}} (2 + 5 k) = \frac{5 n^{2}}{2} + \frac{9 n}{2} + 2$ $S_{9} = 245$ $S_{10} = 297$
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