Find the 13^("th ") term of the geometric sequence 3,-12,48,dots Answer:

Identify type and first term: Identify the type of sequence and the first term (a1). The sequence 3, -12, 48, ... is a geometric sequence because each term is multiplied by a common ratio to get the next term. The first term is a1 = 3.Find common ratio: Find the common ratio (r) of the sequence. To find the common ratio, divide the second term by the first term: r = (-12) / 3 = -4.Use nth term formula: Use the formula for the nth term of a geometric sequence. The formula for the nth term (an) of a geometric sequence is an = a1 * r^(n - 1).Substitute values for 13th term: Substitute the values of a1 and r into the formula to find the 13th term. a13 = 3 * (-4)^(13 - 1) = 3 * (-4)^12.Calculate 13th term: Calculate the 13th term. Since (-4)^12 is a positive number because 12 is an even exponent, we have a13 = 3 * (4^12).Compute 4^12: Compute 4^12. 4^12 = 4^2 * 4^2 * 4^2 * 4^2 * 4^2 * 4^2 = 16 * 16 * 16 * 16 * 16 * 16 = 256 * 256 * 256 = 65536 * 256 = 16777216.Multiply to get 13th term: Multiply 3 by 16777216 to get the 13th term. a13 = 3 * 16777216 = 50331648.

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Find the
13^("th ") term of the geometric sequence
3,-12,48,dots
Answer:

Find the $13^{\text {th }}$ term of the geometric sequence $3,-12,48, \ldots$ $\newline$ Answer:

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Math Problems

Algebra 1

Write variable expressions for geometric sequences

Full solution

Q. Find the

13^{\text {th }}

term of the geometric sequence

3,-12,48, \ldots

\newline

Answer:

Identify type and first term: Identify the type of sequence and the first term ( $a_1$ ). $\newline$ The sequence $3, -12, 48, extellipsis$ is a geometric sequence because each term is multiplied by a common ratio to get the next term. The first term is $a_1 = 3$ .
Find common ratio: Find the common ratio $r$ of the sequence. $\newline$ To find the common ratio, divide the second term by the first term: $r = (-12) / 3 = -4$ .
Use nth term formula: Use the formula for the nth term of a geometric sequence. $\newline$ The formula for the nth term $a_n$ of a geometric sequence is $a_n = a_1 \cdot r^{(n - 1)}$ .
Substitute values for $13$ th term: Substitute the values of $a_1$ and $r$ into the formula to find the $13$ th term. $\newline$ $a_{13} = 3 \times (-4)^{13 - 1} = 3 \times (-4)^{12}.$
Calculate $13$ th term: Calculate the $13^{\text{th}}$ term. $\newline$ Since $(-4)^{12}$ is a positive number because $12$ is an even exponent, we have $a_{13} = 3 \times (4^{12})$ .
Compute $4^{12}$ : Compute $4^{12}$ . $4^{12} = 4^2 \times 4^2 \times 4^2 \times 4^2 \times 4^2 \times 4^2 = 16 \times 16 \times 16 \times 16 \times 16 \times 16 = 256 \times 256 \times 256 = 65536 \times 256 = 16777216$ .
Multiply to get $13$ th term: Multiply $3$ by $16777216$ to get the $13$ th term. $\newline$ $a_{13} = 3 \times 16777216 = 50331648$ .