Write an explicit formula for a_(n), the n^("th ") term of the sequence 6,2,-2,dots Answer: a_(n)=

Find Common Difference: To find the explicit formula for the nth term of the sequence, we first need to determine the common difference by subtracting any term from the term that follows it. Subtract the second term (2) from the first term (6): 6 - 2 = 4 The common difference is -4 (since the sequence is decreasing).Write Explicit Formula: Now that we have the common difference, we can write the explicit formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d where a_1 is the first term and d is the common difference.Substitute Values: Substitute the known values into the formula: a_1 = 6 (the first term) d = -4 (the common difference) a_n = 6 + (n - 1)(-4)Simplify Formula: Simplify the formula: a_n = 6 - 4(n - 1) a_n = 6 - 4n + 4 a_n = 10 - 4n This is the explicit formula for the nth term of the sequence.

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
6,2,-2,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $6,2,-2, \ldots$ $\newline$ Answer: $a_{n}=$

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Math Problems

Algebra 2

Transformations of quadratic functions

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Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

6,2,-2, \ldots

\newline

Answer:

a_{n}=

Find Common Difference: To find the explicit formula for the nth term of the sequence, we first need to determine the common difference by subtracting any term from the term that follows it. $\newline$ Subtract the second term $2$ from the first term $6$ : $\newline$ $6 - 2 = 4$ $\newline$ The common difference is $-4$ (since the sequence is decreasing).
Write Explicit Formula: Now that we have the common difference, we can write the explicit formula for the $n$ th term of an arithmetic sequence: $a_n = a_1 + (n - 1)d$ where $a_1$ is the first term and $d$ is the common difference.
Substitute Values: Substitute the known values into the formula: $\newline$ $a_1 = 6$ (the first term) $\newline$ $d = -4$ (the common difference) $\newline$ $a_n = 6 + (n - 1)(-4)$
Simplify Formula: Simplify the formula: $\newline$ $a_n = 6 - 4(n - 1)$ $\newline$ $a_n = 6 - 4n + 4$ $\newline$ $a_n = 10 - 4n$ $\newline$ This is the explicit formula for the $n$ th term of the sequence.