Maths Problem (Sequence)

[acroviak]

Hello.
Im stuck with 1 question in a mixed set of questions in Sequences

Ill write the question as displayed on the sheet.

"The sequence defined by U1 = 7, Un+1 = 0.2Un + 4 converges to a limit k.

By forming and solving an equation, find the value of k."


The computer writes it in badly, So the U1 should have the 1 in small font, and so should n in Un

Thank you for any input.

Working out would be apprechiated too, so i can learn it :)

[Catron]

U2 = 7*0.2 = 1.4
U3 = 1.4*0.2 = 0.28
etc

Un converges to O, therefore Un +4 converges to 4 and k = 4.

[Catron]

Sorry, not quite right

U2 = 1.4 + 4
U3 = 0.28 + 4
etc

[Catron]

I am sorry - please ignore me, I have just studied this and still I make a pig's ear of it.

[Catron]

Apologies once again but I am unable to copy a Mathcad recurrence system and paste it here.

I expect you already know this but the above sequence is a linear recurrence sequence - and you should be able to find out the closed form of the recurrence system by googling for it.

For what its worth, in your sequence a=7, r=0.2 and d =4, which gives the result 2(0.2)^n-1 +5. The 2(0.2)^n-1 converges to 0, leaving the limit k as 5.

Hope this helps a little.