Write an explicit formula for a_(n), the n^("th ") term of the sequence 1,-4,16,dots Answer: a_(n)=

Identify Pattern: Identify the pattern in the sequence. The given sequence is 1, -4, 16, ... We notice that each term is multiplied by -4 to get the next term. This indicates that the sequence is geometric.Determine Terms: Determine the first term (a_1) and the common ratio (r) of the sequence. The first term, a_1 = 1 To find the common ratio, r, we divide the second term by the first term: r = -4 / 1 = -4Write Formula: Write the explicit formula for the nth term of a geometric sequence. The formula for the nth term of a geometric sequence is: a_n = a_1 * r^(n-1) Substitute the values of a_1 and r into the formula: a_n = 1 * (-4)^(n-1)Simplify: Simplify the formula. The simplified formula for the nth term is: a_n = (-4)^(n-1)

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Write an explicit formula for
a_(n), the
n^("th ") term of the sequence
1,-4,16,dots
Answer:
a_(n)=

Write an explicit formula for $a_{n}$ , the $n^{\text {th }}$ term of the sequence $1,-4,16, \ldots$ $\newline$ Answer: $a_{n}=$

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Math Problems

Algebra 1

Write variable expressions for arithmetic sequences

Full solution

Q. Write an explicit formula for

a_{n}

, the

n^{\text {th }}

term of the sequence

1,-4,16, \ldots

\newline

Answer:

a_{n}=

Identify Pattern: Identify the pattern in the sequence. $\newline$ The given sequence is $1, -4, 16, \ldots$ $\newline$ We notice that each term is multiplied by $-4$ to get the next term. $\newline$ This indicates that the sequence is geometric.
Determine Terms: Determine the first term $a_1$ and the common ratio $r$ of the sequence. $\newline$ The first term, $a_1 = 1$ $\newline$ To find the common ratio, $r$ , we divide the second term by the first term: $\newline$ $r = -4 / 1 = -4$
Write Formula: Write the explicit formula for the nth term of a geometric sequence. $\newline$ The formula for the nth term of a geometric sequence is: $\newline$ $a_n = a_1 \cdot r^{(n-1)}$ $\newline$ Substitute the values of $a_1$ and $r$ into the formula: $\newline$ $a_n = 1 \cdot (-4)^{(n-1)}$
Simplify: Simplify the formula. $\newline$ The simplified formula for the nth term is: $\newline$ $a_n = (-4)^{n-1}$