Sequences & Series: C1

1

Hi People,

I have this question that has stumped me, and I thought you might be able to help me out.

A sequence of terms (Un) is defined n > 1 by the recurrence relation Un+1 = kUn + 2 where k is a constant. Given that U1 = 3:

a) Find an expression in terms of K for U2 (Done that bit...3k + 2)
b) Hence find and expression for U3. Given that U3 = 42
c) Find possible values of k.

Ahhh! I have the answers for b and c, I just don't know how you get to them!

Thanks in advance,

Steve.

Reply 1

generalebriety

16

(b) Well, you know that u_2 = 3k+2. Using the formula you've been given:

u_3 = k(u_2) + 2
and substitute in.

(c) You'll have u_3 = (some quadratic in k). Substitute u_3 = 42 and solve. :smile:

Edit: if my working is correct, you should have k = 10/3 or -4. :smile:

Reply 2

xxrachxx

yellowputty

Hi People,

I have this question that has stumped me, and I thought you might be able to help me out.

A sequence of terms (Un) is defined n > 1 by the recurrence relation Un+1 = kUn + 2 where k is a constant. Given that U1 = 3:

a) Find an expression in terms of K for U2 (Done that bit...3k + 2)
b) Hence find and expression for U3. Given that U3 = 42
c) Find possible values of k.

Ahhh! I have the answers for b and c, I just don't know how you get to them!

Thanks in advance,

Steve.

You do part b exactly as u did part a.
U3= kU2 +2
= k(3k +2) +2
= 3ksq + 2k +2

c) 3ksq +2k +2 = 42
3ksq +2k - 40=0
(3k-10)(k+4)=0
therefore k=-4 or 10/3

Reply 3

Caesium

OP

1

Thanks you so much, both of you! :smile:

Not only have you helped me on that question, I now understand the rest!

Sequences & Series: C1

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