Answer:
Sussanna considered the sequence to be geometric while Paul considered it to be quadratic.
Step-by-step explanation:
The first three terms of a sequence are 1, 2, and 4.
Sussanna considered this sequence as a geometric sequence with first term a=1 and common ratio r=2.
The 8th term of this sequence is given by:
[tex] = a {r}^{7} [/tex]
[tex] = 1 \times {2}^{7} [/tex]
[tex] = 1 \times 128[/tex]
[tex] = 128[/tex]
Paul considered the sequence to be quadratic.
Paul obtained the equation follow:
[tex]a( {1)}^{2} + b(1) + c = 1 \\ a + b + c = 1....(1)[/tex]
[tex]a( {2)}^{2} + b(2) + c = 1 \\ 4a +2 b + c = 2....(2)[/tex]
[tex]a( {3)}^{2} + b(3) + c = 4\\ 9a + 3b + c = 4....(3)[/tex]
He solved the three equations simultaneously to get:
[tex]a = 0.5 \\ b = - 0.5 \\ c = 1[/tex]
He then obtain the rule;
[tex]f(n) = 0.5 {n}^{2} - 0.5n + 1[/tex]
To find the 8th term, he substitute n=8.
[tex]f(8) = 0.5( {8})^{2} - 0.5(8)+ 1 \\ f(8) = 32 - 4 + 1 = 29[/tex]
