Find the 13^("th ") term of the geometric sequence 7,-21,63,dots Answer:

Find Common Ratio: The first term (a1) of the geometric sequence is 7. We need to find the common ratio (r) by dividing the second term by the first term. Calculation: r = -21 / 7 = -3Calculate 13th Term: Now that we have the common ratio, we can find the 13th term (a13) using the formula for the nth term of a geometric sequence: an = a1 * r^(n-1). Calculation: a13 = 7 * (-3)^(13-1) = 7 * (-3)^12Calculate (-3)^12: We need to calculate (-3)^12. Since 12 is an even number, the result will be positive. Calculation: (-3)^12 = 531441Find 13th Term: Now we can find the 13th term by multiplying the first term by (-3)^12. Calculation: a13 = 7 * 531441 = 3720087

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
7,-21,63,dots
Answer:

Find the $13^{\text {th }}$ term of the geometric sequence $7,-21,63, \ldots$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Complex conjugate theorem

Full solution

Q. Find the

13^{\text {th }}

term of the geometric sequence

7,-21,63, \ldots

\newline

Answer:

Find Common Ratio: The first term $a_1$ of the geometric sequence is $7$ . We need to find the common ratio $r$ by dividing the second term by the first term. $\newline$ Calculation: $r = -21 / 7 = -3$
Calculate $13$ th Term: Now that we have the common ratio, we can find the $13$ th term ( $a_{13}$ ) using the formula for the nth term of a geometric sequence: $a_n = a_1 \cdot r^{(n-1)}$ . $\newline$ Calculation: $a_{13} = 7 \cdot (-3)^{13-1} = 7 \cdot (-3)^{12}$
Calculate $(-3)^{12}$ : We need to calculate $(-3)^{12}$ . Since $12$ is an even number, the result will be positive. $\newline$ Calculation: $(-3)^{12} = 531441$
Find $13$ th Term: Now we can find the $13$ th term by multiplying the first term by $(-3)^{12}$ . $\newline$ Calculation: $a_{13} = 7 \times 531441 = 3720087$