Find the 8th term of the geometric sequence shown below. -2x^(3),4x^(6),-8x^(9),dots Answer:

Identify Common Ratio: To find the 8th term of a geometric sequence, we need to identify the common ratio (r) and use the formula for the nth term of a geometric sequence, which is a_n = a_1 * r^(n-1), where a_1 is the first term and n is the term number.Calculate Common Ratio: First, let's find the common ratio by dividing the second term by the first term. r = (4x^(6)) / (-2x^(3)) = -2x^(6-3) = -2x^(3)Find 8th Term: Now that we have the common ratio, we can use it to find the 8th term. a_8 = a_1 * r^(8-1) = a_1 * r^7Substitute Values: Substitute the values we know into the formula. a_8 = (-2x^(3)) * (-2x^(3))^7Simplify Expression: Simplify the expression by calculating the exponent and the multiplication. a_8 = (-2x^(3)) * (128x^(21)) = -256x^(24)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the 8th term of the geometric sequence shown below.

-2x^(3),4x^(6),-8x^(9),dots
Answer:

Find the $8$ th term of the geometric sequence shown below. $\newline$ $-2 x^{3}, 4 x^{6},-8 x^{9}, \ldots$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Find trigonometric functions using a calculator

Full solution

Q. Find the

8

th term of the geometric sequence shown below.

\newline

-2 x^{3}, 4 x^{6},-8 x^{9}, \ldots

\newline

Answer:

Identify Common Ratio: To find the $8^{th}$ term of a geometric sequence, we need to identify the common ratio $(r)$ and use the formula for the $n^{th}$ term of a geometric sequence, which is $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $n$ is the term number.
Calculate Common Ratio: First, let's find the common ratio by dividing the second term by the first term. $\newline$ $r = \frac{4x^{6}}{-2x^{3}} = -2x^{6-3} = -2x^{3}$
Find $8^{\text{th}}$ Term: Now that we have the common ratio, we can use it to find the $8^{\text{th}}$ term. $a_8 = a_1 \times r^{(8-1)} = a_1 \times r^7$
Substitute Values: Substitute the values we know into the formula. $\newline$ $a_8 = (-2x^{3}) \cdot (-2x^{3})^7$
Simplify Expression: Simplify the expression by calculating the exponent and the multiplication. $a_8 = (-2x^{3}) \times (128x^{21}) = -256x^{24}$