Question

Find the 14th term of the geometric sequence 5, -10, 20 (PLEASEE HELP)

Answer 1

Answer:

$a_{14}=-40960$

Step-by-step explanation:

General form of a geometric sequence:

  $a_n=ar^{n-1}$

where:

• $a_n$ is the nth term.
• a is the first term.
• r is the common ratio.

Given sequence:

• 5, -10, 20, ...

First term

$a=5$

Common ratio

To find the common ratio r, divide consecutive terms:

$\implies r=\dfrac{-10}{5}=-2$

Substitute the found values of a and r into the formula to create an equation for the nth term:

$\implies a_n=5(-2)^{n-1}$

To find the 14th term, substitute n = 14 into the found equation:

$\implies a_{14}=5(-2)^{14-1}$

$\implies a_{14}=5(-2)^{13}$

$\implies a_{14}=5(-8192)$

$\implies a_{14}=-40960$

Therefore, the 14th term of the given geometric sequence is -40960.

Learn more about geometric sequences here:

https://brainly.com/question/25398220

https://brainly.com/question/27783194