Find the 8th term of the geometric sequence shown below. -2x^(8),-4x^(10),-8x^(12),dots Answer:

Identify common ratio: Identify the common ratio (r) of the geometric sequence by dividing the second term by the first term. Calculation: r = (-4x^(10)) / (-2x^(8)) Simplification: r = 2x^(2)Use nth term formula: 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. Calculation: a_8 = (-2x^(8)) * (2x^(2))^(8-1) Simplification: a_8 = (-2x^(8)) * (2x^(2))^7Simplify 8th term: Simplify the expression for the 8th term by calculating the exponent and multiplication. Calculation: a_8 = (-2x^(8)) * (128x^(14)) Simplification: a_8 = -256x^(22)

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^(8),-4x^(10),-8x^(12),dots
Answer:

Find the $8$ th term of the geometric sequence shown below. $\newline$ $-2 x^{8},-4 x^{10},-8 x^{12}, \ldots$ $\newline$ 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^{8},-4 x^{10},-8 x^{12}, \ldots

\newline

Answer:

Identify common ratio: Identify the common ratio $r$ of the geometric sequence by dividing the second term by the first term. $\newline$ Calculation: $r = \frac{-4x^{10}}{-2x^{8}}$ $\newline$ Simplification: $r = 2x^{2}$
Use nth term formula: Use the formula for the nth 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. $\newline$ Calculation: $a_8 = (-2x^{8}) \cdot (2x^{2})^{8-1}$ $\newline$ Simplification: $a_8 = (-2x^{8}) \cdot (2x^{2})^7$
Simplify $8$ th term: Simplify the expression for the $8$ th term by calculating the exponent and multiplication. $\newline$ Calculation: $a_8 = (-2x^{8}) \times (128x^{14})$ $\newline$ Simplification: $a_8 = -256x^{22}$