Technology0 min ago
Maths Problem (Sequence)
4 Answers
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 :)
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 :)
Answers
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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.
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.
1 to 4 of 4
