Find the 8^th term of the geometric sequence 7,-21,63,dots Answer:

Find First Term and Ratio: To find the 8th term of a geometric sequence, we need to know the first term and the common ratio. The first term (a1) is given as 7. To find the common ratio (r), we divide the second term by the first term. r = (-21) / 7Calculate Common Ratio: Now, let's calculate the common ratio using the values from the previous step. r = (-21) / 7 = -3 The common ratio is -3.Use Formula for 8th Term: With the first term and the common ratio, we can find the nth term of the geometric sequence using the formula an = a1 * r^(n-1). For the 8th term (a8), we plug in the values: a8 = 7 * (-3)^(8-1)Calculate 8th Term: Now we calculate the 8th term using the values from the previous step. a8 = 7 * (-3)^7 a8 = 7 * (-2187)Finally, we multiply 7 by -2187 to find the 8th term. a8 = 7 * (-2187) = -15309

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the 8^th term of the geometric sequence
7,-21,63,dots
Answer:

Find the $8^{\text {th }}$ term of the geometric sequence $7,-21,63, \ldots$ $\newline$ Answer:

View step-by-step help

Full solution

Q. Find the

8^{\text {th }}

term of the geometric sequence

7,-21,63, \ldots

\newline

Answer:

Find First Term and Ratio: To find the $8^{\text{th}}$ term of a geometric sequence, we need to know the first term and the common ratio. The first term ( $a_1$ ) is given as $7$ . To find the common ratio ( $r$ ), we divide the second term by the first term. $\newline$ $r = \frac{-21}{7}$
Calculate Common Ratio: Now, let's calculate the common ratio using the values from the previous step. $\newline$ $r = (-21) / 7 = -3$ $\newline$ The common ratio is $-3$ .
Use Formula for $8$ th Term: With the first term and the common ratio, we can find the $n$ th term of the geometric sequence using the formula $a_n = a_1 \times r^{(n-1)}$ . For the $8$ th term ( $a_8$ ), we plug in the values: $\newline$ $a_8 = 7 \times (-3)^{(8-1)}$
Calculate $8$ th Term: Now we calculate the $8$ th term using the values from the previous step. $\newline$ $a_8 = 7 \times (-3)^7$ $\newline$ $a_8 = 7 \times (-2187)$
Calculate $8$ th Term: Now we calculate the $8$ th term using the values from the previous step. $\newline$ $a_8 = 7 \times (-3)^7$ $\newline$ $a_8 = 7 \times (-2187)$ Finally, we multiply $7$ by $-2187$ to find the $8$ th term. $\newline$ $a_8 = 7 \times (-2187) = -15309$