Question

Identify the 19th term of a geometric sequence where a1 = 14 and a9 = 358.80. Round the common ratio and 19th term to the nearest hundredth.
I know that I need to find r first which I got r^8=25.63 then you have to do the square root of each side but I can't remember how to solve when you have the square root of a number and then a number on the outside of the square root in the little check mark part.

Answer 1

if we divide it all by 14; we normalize it i believe

Answer 2

a1 = 14 and a9 = 358.80
------------------------ ; a1 = 1 and a9 = 25.6286
14

a9 = r^8

r = 25.6286^(1/8) = about 1.499997

Answer 3

^8 and 8rt cancel each other

Answer 4

8rt(n) = n^(1/8)

Answer 5

I don't think thats right. I just need to know how to get an answer when I come across something like r^8=25.63 and then I have to sq each side I just don't know how to do it when there is a number on the outside in this case is 8 in the check mark part of the sq root symbol.

Answer 6

\[\LARGE \begin{array}{l}{a_9} = {a_1} \cdot {r^{9 - 1}}\\358.80 = 14 \cdot {q^8}\\25.62 = {q^8}\\q = \pm 1.49\\\\{a_9} = {a_1} \cdot 1.49\\358.80 = 14 \cdot {(1.49)^8}\\358.80 = 14 \cdot 24.29\\358.80 = 340.06\end{array}\]
it should be \[ \approx \]
I just tried if q=+
and it worked pretty much...
(the reason why numbers doesn't fit is because I didn't use more than 2 decimals)
I guess you have to try it...

Answer 7

Is there a button on the scientific calculator I can use? to figure out the sq root thing?

Answer 8

well I don't know what kind of calculator you have: (In pc) I have\use Microsoft mathematics.... and there I just type q^8= something... and it finds that...

Answer 9

A scientific one

Answer 10

your asking how to turn a undo a ^8 right?

Answer 11

I know I never said that I found a_19 I just used a_9 to see if q=+1.49 works...
if it was - there would be
358 =-340
and that's not true...
but now to find a19
just substitute into the formula
\[\LARGE a_{19}=a_1\cdot r^{19-1} \]