Find-the-nth-term-of-the-sequence-a-1-2-1-4-1-8-7-62-b-1-2-1-4-1-8-0-

Question Number 56594 by Joel578 last updated on 19/Mar/19

Find the n th term of the sequence

(a) \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{7}{62}, \dots

(b) \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, 0, \dots

Answered by MJS last updated on 19/Mar/19

there are always \infty possibilities

with four terms given, we can match with

x_{n} = c_{3} n^{3} + c_{2} n^{2} + c_{1} n + c_{0}

(or any other model with 4 independent

constants)

we get

(a) x_{n} = - \frac{1}{496} n^{3} + \frac{37}{496} n^{2} - \frac{57}{124} n + \frac{55}{62}

(b) x_{n} = - \frac{1}{48} n^{3} + \frac{3}{16} n^{2} - \frac{2}{3} n + 1

Commented by Joel578 last updated on 19/Mar/19

t h a n k y o u s i r M J S

b u t, w h i c h f o r m u l a d i d u h a v e u s e d ?

I m e a n, t h e c h a p t e r t h a t s t u d y i n g t h i s f o r m u l a

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