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pochemuha
3 years ago
11

Write the explicit formula for the arithmetic sequence.

Mathematics
1 answer:
qwelly [4]3 years ago
3 0

Option C

The explicit formula for the arithmetic sequence is a_n = 9 - 6n

<em><u>Solution:</u></em>

Given that the arithmetic sequence is:

3, -3, -9, -15, -21, ...

To find: Explicit formula for the arithmetic sequence

<em><u>The nth term of an arithmetic sequence is given by:</u></em>

a_n = a_1 + (n - 1)d

Where a_n is nth term of sequence

n is the term's location

a_1 is the first term of sequence

d is the common difference between terms

In an arithmetic sequence, the difference between successive terms is constant. This means that we can move from any term to the next one by adding a constant value.

In the given sequence:

3, -3, -9, -15, -21, ...

a_1 = \text{ first term } = 3

d = difference between any two terms in sequence

d = a_2 - a_1

d = -3 - (3) = -6

Substituting the values in above formula,

a_n = 3 + (n - 1)(-6)\\\\a_n = 3 -6n + 6\\\\a_n = 9 - 6n

Thus the explicit formula to find any term in sequence is found

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Step-by-step explanation:

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Step-by-step explanation:

The standard form will look like ...

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<em>Additional comment</em>

In general, "standard form" is ax²+bx+c. In this case, the coefficient 'a' can be 1 since neither of the roots is expressed as a fraction. The sum of roots is (-b/a) and the product of roots is (c/a).

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