Find the 13^("th ") term of the geometric sequence 1,-3,9,dots Answer:

Identify Geometric Sequence: The given sequence is a geometric sequence, which means each term after the first is found by multiplying the previous term by a common ratio (r). To find the 13th term, we need to identify the common ratio and use the formula for the nth term of a geometric sequence, which is a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, and r is the common ratio.Find Common Ratio: We can find the common ratio by dividing the second term by the first term. So, r = -3 / 1 = -3.Calculate 13th Term: Now that we have the common ratio, we can use the formula to find the 13th term. Plugging in the values, we get a_13 = 1 * (-3)^(13-1) = 1 * (-3)^12.Calculating (-3)^12, we get 531441, since (-3)^12 means multiplying -3 by itself 12 times, and a negative number raised to an even power results in a positive number.Therefore, the 13th term of the sequence is a_13 = 1 * 531441 = 531441.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the
13^("th ") term of the geometric sequence
1,-3,9,dots
Answer:

Find the $13^{\text {th }}$ term of the geometric sequence $1,-3,9, \ldots$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Calculus

Find indefinite integrals using the substitution

Full solution

Q. Find the

13^{\text {th }}

term of the geometric sequence

1,-3,9, \ldots

\newline

Answer:

Identify Geometric Sequence: The given sequence is a geometric sequence, which means each term after the first is found by multiplying the previous term by a common ratio $r$ . To find the $13^{\text{th}}$ term, we need to identify the common ratio and use the formula for the $n^{\text{th}}$ term of a geometric sequence, which is $a_n = a_1 \times r^{(n-1)}$ , where $a_n$ is the $n^{\text{th}}$ term, $a_1$ is the first term, and $r$ is the common ratio.
Find Common Ratio: We can find the common ratio by dividing the second term by the first term. So, $r = \frac{-3}{1} = -3$ .
Calculate $13$ th Term: Now that we have the common ratio, we can use the formula to find the $13$ th term. Plugging in the values, we get $a_{13} = 1 \times (-3)^{13-1} = 1 \times (-3)^{12}$ .
Calculate $13$ th Term: Now that we have the common ratio, we can use the formula to find the $13$ th term. Plugging in the values, we get $a_{13} = 1 \times (-3)^{13-1} = 1 \times (-3)^{12}$ . Calculating $(-3)^{12}$ , we get $531441$ , since $(-3)^{12}$ means multiplying $-3$ by itself $12$ times, and a negative number raised to an even power results in a positive number.
Calculate $13$ th Term: Now that we have the common ratio, we can use the formula to find the $13$ th term. Plugging in the values, we get $a_{13} = 1 \times (-3)^{13-1} = 1 \times (-3)^{12}$ . Calculating $(-3)^{12}$ , we get $531441$ , since $(-3)^{12}$ means multiplying $-3$ by itself $12$ times, and a negative number raised to an even power results in a positive number. Therefore, the $13$ th term of the sequence is $a_{13} = 1 \times 531441 = 531441$ .