Question

What is the third term of the sequence

defined by the formula t₁ = 2a,
t₂ = 3a - 1, and tn = 2tn-1- 3tn-2 + 1
when n ≥ 3?
A) -1
B) -9a +2
C) 2
D) -5a +3

Answer 1

A) -1

Explanation:

You want the third term in the recursively-defined sequence ...

`\begin{cases}t_1=2a\\t_2=3a-1\\t_n=2t_(n-1)-3t_(n-2)+1\end{cases}`

Third term

The third term is given by the sequence definition:

`t_3=2t_2-3t_1+1\\\\t_3=2(3a-1)-3(2a)+1\\\\t_3=6a-2-6a+1\\\\\boxed{t_3 = -1}`

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Additional comment

The attachment shows the first 5 terms.