Finding the explicit formula for the sequence 2, -2, -6, -10, -14, . . .

Express the terms of the following sequence by giving an explicit formula.2, -2, -6, -10, -14, . . .

To find an explicit formula for the given sequence 2, -2, -6, -10, -14,

To find an explicit formula for the given sequence 2, -2, -6, -10, -14, . . . we can observe that each term is obtained by subtracting 4 from the previous term.

Let’s denote the position of a term in the sequence by the variable n, where n starts at 1. The first term corresponds to n = 1, the second term to n = 2, and so on.

We can start by finding the relationship between the position of a term and its value.

Term 1: 2
Term 2: 2 – 4 = -2
Term 3: -2 – 4 = -6
Term 4: -6 – 4 = -10
Term 5: -10 – 4 = -14

From this pattern, we can observe that each term is given by the formula:
Tn = 2 – 4(n-1)

Here, Tn represents the nth term in the sequence. By substituting the appropriate value of n, we can find any term in the sequence. For example:

The 7th term (n = 7):
T7 = 2 – 4(7-1)
T7 = 2 – 4(6)
T7 = 2 – 24
T7 = -22

Therefore, the explicit formula for the given sequence is:
Tn = 2 – 4(n-1)

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