Express the terms of the following sequence by giving an explicit formula.2, -2, -6, -10, -14, . . .
To find an explicit formula for a sequence, we need to identify the pattern or rule that generates each term of the sequence
To find an explicit formula for a sequence, we need to identify the pattern or rule that generates each term of the sequence.
Looking at the given sequence: 2, -2, -6, -10, -14, …
We can observe that each term is obtained by subtracting 4 from the previous term.
So, the explicit formula for this sequence can be written as:
aₙ = aₙ₋₁ – 4
Here, aₙ represents the nth term of the sequence, and aₙ₋₁ represents the previous term.
To find any specific term in the sequence, you can start with the first term (2), and continually subtract 4 from the previous term.
For example:
To find the 5th term (a₅):
a₅ = a₄ – 4
= -14 – 4
= -18
Therefore, the 5th term in the sequence is -18.
Using the same method, you can find any term in this sequence by substituting the appropriate value for n into the explicit formula.
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