Let consider the following sequence : 1 , 3 , (√(17)) , 5 , (√(33)) , (√(41)) , ... What may be the explicit formula that can gives this sequence of number ? Thank you


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Question Number 56426 by Hassen_Timol last updated on 16/Mar/19

$L e t c o n s i d e r t h e f o l l o w i n g s e q u e n c e :$ $1, 3, \sqrt{17}, 5, \sqrt{33}, \sqrt{41}, . . .$ $W h a t m a y b e t h e e x p l i c i t f o r m u l a t h a t$ $c a n g i v e s t h i s s e q u e n c e o f n u m b e r ?$ $T h a n k y o u$
	Answered by kaivan.ahmadi last updated on 16/Mar/19

	$\sqrt{1}, \sqrt{9}, \sqrt{17}, \sqrt{25}, \sqrt{33}, \sqrt{41}, . . .$ $b = 1, d = 8$ $b_{n} = a + (n - 1) d = 1 + (n - 1) 8 = 8 n - 7$ $a_{n} = \sqrt{8 n - 7}$
	Commented by Hassen_Timol last updated on 16/Mar/19

	$T h a n k y o u, I {d i d n}^{'} t t h i n k a b o u t t h i s m e t h o d . . .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 16/Mar/19

	$\sqrt{1}, \sqrt{9}, \sqrt{17}, \sqrt{25}, \sqrt{33}^{'} \sqrt{41} . .$ $T_{n} = \sqrt{1 + (n - 1) 8} \to \sqrt{8 n - 7}$
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