A sequence is generated by the recurrence relation $$u_{n+1} = mu_n + c$$ where the first three terms of the sequence are 6, 9 and 11; (a) Find the values of m and c - Scottish Highers Maths - Question 4 - 2022

To solve for the constants m and c, we can set up a system of equations using the given terms of the sequence:

1. For the first term (when n=1): $u_2 = mu_1 + c$
   Substituting the values:
   $9 = 6m + c$
   (Equation 1)

2. For the second term (when n=2): $u_3 = mu_2 + c$
   Substituting the values:
   $11 = 9m + c$
   (Equation 2)

Next, we can solve these equations simultaneously:

From Equation 1, we can express c: $c = 9 - 6m$

Substituting this value of c into Equation 2: $11 = 9m + (9 - 6m)$
$11 = 3m + 9$
$3m = 2$
m = rac{2}{3}

Now substituting the value of m back into Equation 1 to find c: c = 9 - 6(rac{2}{3})
$c = 9 - 4 = 5$

Thus, the values are: $m = \frac{2}{3}, c = 5$