0-5-4-4-5-how-to-solution-aritmatic-

Question Number 135689 by joki last updated on 15/Mar/21

0, \dots ., \dots ., \frac{5}{4}, \frac{4}{5}, \dots .

how to solution aritmatic

Commented by liberty last updated on 15/Mar/21

A P ?

Commented by joki last updated on 15/Mar/21

common difference and sum

Commented by mr W last updated on 15/Mar/21

i f i t i s a n A P, t h e n t h e c o m m o n

d i f f e r e n c e i s \frac{4}{5} - \frac{5}{4} = - \frac{9}{20}

t h a t m e a n s t h e A P i s d e c r e a s i n g!

a l l t e r m s b e f o r e t h e t e r m \frac{4}{5} m u s t

b e l a r g e r t h a n \frac{4}{5}, t h i s i s n o t t h e c a s e,

s i n c e t h e f i r s t t e r m i s 0, w h i c h i s

s m a l l e r t h a n \frac{4}{5} . t h e r e f o r e t h e

q u e s t i o n i s b a d, {i t}^{'} s n o t a n A P, b u t

w h a t i t i s, i s n o t c l e a r .

Commented by MJS_new last updated on 15/Mar/21

assuming 3 points given

P_{1} = (\begin{matrix} 1 \\ 0 \end{matrix}) P_{2} = (\begin{matrix} 4 \\ 5 / 4 \end{matrix}) P_{3} = (\begin{matrix} 5 \\ 4 / 5 \end{matrix})

y = {a x}^{2} + b x + c

(1) 0 = a + b + c

(2) \frac{5}{4} = 16 a + 4 b + c

(3) \frac{4}{5} = 25 a + 5 b + c

solving this system I get

a = - \frac{13}{60} \land b = \frac{3}{2} \land c = - \frac{77}{60}

y = - \frac{13}{60} x^{2} + \frac{3}{2} x - \frac{77}{60}

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