contestada

b) Another sequence is defined using this term-to-term rule, Un+1 = kun + r where k and rare constants. Given that u₁ = 37, U₂= 188 and u3 = 943, find the value of k and the value of r. b ) Another sequence is defined using this term - to - term rule , Un + 1 = kun + r where k and rare constants . Given that u₁ = 37 , U₂ = 188 and u3 = 943 , find the value of k and the value of r .​

Respuesta :

varshamittal029

The values of k and r are given by 5 and 3 respectively.

Here in this problem it is given that,

General formula for the sequence is given by,

[tex]U_{n+1}=kU_n+r[/tex]

First term of the sequence, [tex]U_1=37[/tex]

Second term,

[tex]U_2=188[/tex]

[tex]U_{1+1}=188[/tex], rearranging

[tex]kU_1+r=188[/tex], applying general formula

[tex]37k+r=188[/tex]..........(1)

Third term,

[tex]U_3=943[/tex]

[tex]U_{2+1}=943[/tex], rearranging

[tex]kU_2+r=943[/tex], applying general formula

[tex]188k+r=943[/tex]..........(2)

Now (2) - (1) we get,

188k+r-37k-r = 943-188

151k = 755

k = 755/151 = 5

Hence the value of k is 5.

Substituting the value of k in (1) we get,

37*5+r = 188

185+r = 188

r = 188-185 = 3

Thus the value of r is 3.

Learn more about Sequence here -

https://brainly.com/question/1275192

#SPJ10

Otras preguntas