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-

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}, \dots

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}, \dots

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 \dots

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}