Question

1.Find the first 3 terms of the geometric sequence with
a6=-128 and a11=4,096
2.Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor,it rebounds to 85% of its previous height.How high will the ball rebound after its third bounce? Round to the nearest tenth.

Answer 1

@jdoe0001 could you help me?

Answer 2

\(\large { \begin{array}{llll}
term&value\\
\hline\\
6&-128\\
7&-128\cdot {\color{red}{ r}}\\
8&(-128\cdot {\color{red}{ r}})\cdot {\color{red}{ r}}\\
9&(-128\cdot {\color{red}{ r\cdot r}})\cdot {\color{red}{ r}}\\
10&(-128\cdot {\color{red}{ r\cdot r\cdot r}})\cdot {\color{red}{ r}}\\
11&4096\implies (-128\cdot {\color{red}{ r\cdot r\cdot r\cdot r\cdot r}})\implies -128r^5
\end{array}
\\ \quad \\
\implies 4096=-128r^5 }\)

so to find "r", or the "common ratio", solve for "r"

once you find "r", then use that in the geometric sequence to get 1st term

once you have the 1st term, and "r", then you can pretty much get any term

Answer 3

What is the exact formula you use to solve for R? I know what "r" is I just don't know what the general formula is for R? @jdoe0001

Answer 4

\(\Large a_{\color{blue}{ n}}=a_1\cdot {\color{red}{ r}}^{{\color{blue}{ n}}-1}\)

Answer 5

what did you get for "r" anyway?

Answer 6

-2? and thanks

Answer 7

@jdoe0001

Answer 8

ohh ... yes so
we know "r = -2" and we also know that the 6th term is -128

so \(\bf a_{\color{blue}{ 6}}=a_1\cdot {\color{red}{ r}}^{{\color{blue}{ 6}}-1}\implies -128=a_1\cdot {\color{red}{ -2}}^5\implies \cfrac{-128}{-2^5}=a_1 \iff 64\)

Answer 9

woops...64 ahemm.. heheh... is not that... anyhhow...

Answer 10

\(\bf a_{\color{blue}{ 6}}=a_1\cdot {\color{red}{ r}}^{{\color{blue}{ 6}}-1}\implies -128=a_1\cdot {\color{red}{ -2}}^5\implies \cfrac{-128}{-2^5}=a_1
\\ \quad \\
\cfrac{-128}{-32}=a_1 \iff 4\)

Answer 11

wait doesn't \[a_{1}\]=21? @jdoe0001

Answer 12

\(\bf a_{\color{blue}{ 6}}=a_1\cdot {\color{red}{ r}}^{{\color{blue}{ 6}}-1}\implies -128=a_1\cdot {\color{red}{ -2}}^5\implies \cfrac{-128}{-2^5}=a_1
\\ \quad \\
\bbox[border: 1px solid black]{ \cfrac{-128}{-32}=a_1 \iff 4 } \)

Answer 13

what's the double arrow represent?

Answer 14

@jdoe0001

Answer 15

nevermind sorry I figured it out.