A sequence is generated by the recurrence relation t_{n+1} = mt_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 - 2019

To find the values of $m$ and $c$, we need to use the given sequence and the recurrence relation:

1. Using the first two terms:

   • For $n=1$:

   $t_2 = mt_1 + c$ $9 = m(6) + c$

   Hence, we can write: $6m + c = 9 \ (1)$

2. Using the second and third terms:

   • For $n=2$:

   $t_3 = mt_2 + c$ $11 = m(9) + c$

   This gives us: $9m + c = 11 \ (2)$

3. Subtracting equations (1) from (2):

   • We get: $(9m + c) - (6m + c) = 11 - 9$ $3m = 2$ m = rac{2}{3}

4. Substituting m back into one of the equations:

   • Using equation (1):

   6(rac{2}{3}) + c = 9 $4 + c = 9$ $c = 5$

Thus, the values are:

• $m = \frac{2}{3}$
• $c = 5$.