If-y-n-1-y-n-6-and-y-0-7-Find-y-n-

Question Number 95014 by I want to learn more last updated on 22/May/20

If y_{n + 1} - y_{n} = 6, and y_{0} = 7

Find y_{n}

Commented by prakash jain last updated on 22/May/20

This is an arithmetic progression :

y_{0} = 7

y_{n + 1} = y_{n} + 6

firzt term 7

common difference = 6

y_{n} = 7 + n 6

Commented by I want to learn more last updated on 22/May/20

Sir, with y_{n} = a + (n - 1) d, i did not get it .

y_{n} = 7 + (n - 1) . 6 = 7 + 6 n - 6 = 6 n + 1

Commented by I want to learn more last updated on 22/May/20

And sir

for y_{n - 2} + y_{n - 1} + y_{n} = 0

auxilliary equation is : x^{2} + x + 1 = 0

What of

y_{n + 2} + y_{n + 3} + y_{n - 1} + y_{n} = 0

what is the auxilliary equation

Commented by mr W last updated on 22/May/20

“ y o u w a n t t o l e a r n {m o r e}^{″} s i r :

t r y t o l e a r n t h i n g s o n e a f t e r a n o t h e r!

i f y o u a r e s t i l l a t t h e l e v e l f o r A P,

f o r g e t a t f i r s t “ a u x i l l i a r y {e q u a t i o n}^{″} .

b a c k t o y o u r o r i g i n a l q u e s t i o n :

y o u s h o u l d m a k e c l e a r w h a t y o u m e a n

w i t h “ n^{″} . i f y o u s a y y_{n} = 6 n + 1, b u t

y o u g a v e y o u r f i r s t t e r m y_{0}, t h e n

y o u a r e w r o n g, s i n c e y_{0} = 6 \times 0 + 1 = 1 \neq 7 .

c o r r e c t i s y_{n} = 6 n + 7 . s o n e v e r j u s t

l e a r n a f o r m u l a, b u t l e a r n w h a t i s

b e h i n d i t!

Commented by I want to learn more last updated on 22/May/20

Thanks sir .

Commented by I want to learn more last updated on 22/May/20

But i got the question from the auxilliary equations

Commented by prakash jain last updated on 22/May/20

You may want to just do a internet

search on “ recurrence {relation}^{″} .

You will find some general techinques

on how to solve recurrence relation .

Sometime you have to do a variable

subtituion to convert to linear

recurrence (ex . Q 93173)

Commented by I want to learn more last updated on 22/May/20

I can express negative base like

y_{n - 2} + y_{n - 1}

but i cannot find aucilliary of

y_{n + 2} + y_{n + 3} + \dots for positive base and negative together .

Commented by prakash jain last updated on 22/May/20

What matter is a difference say

for example

y_{n + 2} = 5 y_{n} + 3 y_{n + 1}

Subtitue n = n - 2

y_{n} = 5 y_{n - 2} + 3 y_{n - 1}

Commented by I want to learn more last updated on 22/May/20

I appreciate . now i have an idea .

Thanks for your time .