What is the explicit formula for the arithmetic sequence -7.5, -9, -10.5, -12, ....?

Solution:

Given,

Sequence -7.5, -9, -10.5, -12, .... is arithmetic.

An arithmetic sequence is a list of numbers with a definite pattern.

If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

Explicit formula : a_n = a₁(n - 1)d

a₁ = First term

d = common difference.

Here,

a₁ = -7.5,

d = -9 - (-7.5) = -1.5

a_n = -7.5 + (n - 1) (-1.5)

a_n = -7.5 - 1.5(n - 1)

Therefore, a_n = -7.5 - 1.5(n - 1)

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What is the explicit formula for the arithmetic sequence -7.5, -9, -10.5, -12, ....?

Summary:

The explicit formula for the arithmetic sequence -7.5, -9, -10.5, -12, .... is a_n = -7.5 - 1.5(n - 1).