Question

Wyznacz i r ciągu arytmetycznego (an), jeśli

a)

b) wyznacz a ciągu geometrycznego (an)

jeśli a_{1}

DAJE NAJ

Answer 1

а)

 

{a10 - 2*a7 = -5

{a6 - 2*a4 = 1

 

{a1+9r-2*(a1+6r) = -5

{a1+5r - 2*(a1+3r) = 1

 

{-a1-2r = -5  /*(-1)
{-a1-r = 1

 

+ {a1+2r=5
+ {-a1-r = 1

==========

r = 6

 

a1 = 5-2r = 5-2*6 = 5-12 = -7

 

 

b)

{a1+a3 = 39

{a2+a4 = 26

 

{a1 + a1*q^2 =39
{a1*q^1 + a1*q^3 = 26

 

{a1* (1+q^2) = 39
{a1 * (q + q^3) = 26

 

{ a1 = 39/(1+q^2)
{ 39(q + q^3) /(1+q^2) = 26  (*)

 

(*)

 

26+26q^2 = 39q + 39q^3

 

q= 2/3

 

a1 = 39/(1+q^2) = 39/(9/9+4/9) = 39/ (13/9)  = 27