To find the second, third, and fourth terms, we will substitute 2,3, and 4 in the above formula. To do so, we will use a table.
n
A(n)=A(n−1)−4
A(n)
1
A(1)=8
2
A(2)=A(2−1)−4
A(2)=A(1)−4 ⇕ A(2)=8−4=4
3
A(3)=A(3−1)−4
A(3)=A(2)−4 ⇕ A(3)=4−4=0
4
A(4)=A(4−1)−4
A(4)=A(3)−4 ⇕ A(4)=0−4=-4
Therefore, the next three terms of the sequence are 4,0, and -4. We also want to find the explicit formula of this arithmetic sequence. It combines the information provided by the two equations of the recursive form into a single equation.
In these formulas, d is the common difference and A(1) is the first term. Looking once again at the given recursive formula, we can identify the common difference d and the value of the first term A1.
A(n)=A(n−1)−4;A(1)=8
We can see that the common difference is -4 and the first term is 8. Now we have enough information to write an explicit formula for this sequence.
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