How many seconds are there in (a) one hour and thirty-five minutes and (b) one day?

Write an<br> explicit formula for An, the nth term of the sequence 7, -42, 252, ....

erik [133]

Answer:

$A_n = 7(-6)^{n-1}$

Step-by-step explanation:

<u>Key skills needed: Explicit formula, Geometric sequence</u>

1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.

This can be done by doing -42 ÷ 7 or 252 ÷ -42

-42 ÷ 7 equals -6.

252 ÷ -42 also equals -6.

2) This means that constant is -6.

3) The general form for an explicit formula of a geometric sequence is:

$a_n = a_1(r)^{n-1}$

--> r means the constant (or common ratio) that is being multiplied.

--> $a_1$ means the first term

--> $a_n$ means the "nth" numbered term (so $a_3$ is the 3rd term, $a_{10}$ is the 10th term and so on).

--> $n-1$ is just the "n" in $a_n$ minus 1.

4) We can use this formula to create an explicit formula for the geometric sequence in the problem.

--> $r = -6$ (Since we got -6 as the constant/common ratio).

--> $a_1 = 7$ (Since 7 is the 1st term)

This means that our formula would be --> $A_n = 7(-6)^{n-1}$

<em>Hope you understood and have a nice day!! :D</em>

8 0

3 years ago

Use the Law of Sines to find the measure of angle J to the nearest degree.

rjkz [21]

$\bf \textit{Law of sines}
\\ \quad \\
\cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c}\\\\
-----------------------------\\\\
\cfrac{sin(J)}{9.1}=\cfrac{sin(97^o)}{11}\implies sin(J)=\cfrac{9.1\cdot sin(97^o)}{11}
\\\\\\
\textit{now taking }sin^{-1}\textit{ to both sides}
\\\\\\
sin^{-1}\left[ sin(J) \right]=sin^{-1}\left( \cfrac{9.1\cdot sin(97^o)}{11} \right)
\\\\\\
\measuredangle J=sin^{-1}\left( \cfrac{9.1\cdot sin(97^o)}{11} \right)$