## 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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