Need help with an exercise

Romsek said:
[MATH]a_k = a_1 r^{k-1}\\~\\ a_6 = a_1 r^5 = 64\\ a_{15} = a_1 r^{14} = 386[/MATH]
Can you solve those for \(\displaystyle a_1,~r\) ?
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I tried but apparently every single one of my attempts were wrong. I could really use the answer

Ty for helping
 
UnlinkedNebula said:
I tried but apparently … my attempts were wrong …
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Hello UN. Please confirm that you posted the exercise correctly. As it is, the Real values for a1 and r are Irrational. They won't yield Whole-number terms like 64 and 386. (For example, were we to round approximations for a1 and r to eight decimal places, we'd get terms like 64..00000001 and 386.0000003).

Rounded decimal approximations:

a1 is about 23.58415638

r is about 1.220989490

If you posted correctly, then your materials probably contain a mistake.

?
 
UnlinkedNebula said:
I tried but apparently every single one of my attempts were wrong. I could really use the answer

Ty for helping
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If you let a be the first term and r the common ratio:
\(\displaystyle ar^5 = 64\)
\(\displaystyle ar^{14} = 386\)

If you divide these equations you get:
\(\displaystyle \frac{ar^{14}}{ar^5} = \frac{386}{64}\)

Simplify both sides and ....
 
Otis said:
Hello UN. Please confirm that you posted the exercise correctly. As it is, the Real values for a1 and r are Irrational. They won't yield Whole-number terms like 64 and 386. (For example, were we to round approximations for a1 and r to eight decimal places, we'd get terms like 64..00000001 and 386.0000003).

Rounded decimal approximations:

a1 is about 23.58415638

r is about 1.220989490

If you posted correctly, then your materials probably contain a mistake.

?
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Exactly, I got decimals every single time I tried so I thought I was doing something wrong. I will ask my professor once I get to class to see if he made a mistake when writing down the homework.

Ty
 
UnlinkedNebula said:
I tried but apparently every single one of my attempts were wrong. I could really use the answer

Ty for helping
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Sorry but we do not give answers on this forum. There are a number of places online that would do this for a fee. We prefer to help the student arrive at the answer on their.

If you had read the forum's guideline and showed us your work we would have told you where you made your mistake and you would be done with this problem by now.
 
UnlinkedNebula said:
I tried but apparently every single one of my attempts were wrong. I could really use the answer

Ty for helping
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It's possible that their answer (or the question itself) is wrong, or that you just didn't enter the answer in the appropriate form (whether this is being judged by a computer, as I assume, or by a teacher). If you told us what answers you entered, and showed us the exact statement of the problem as given to you, including instructions such as "in fraction form" or "to two decimal places" or whatever). The more you give us, the quicker we can help.

We'd love to help more, but you haven't yet made that possible.
 
I'm a bit confused, why does a and r be decimal or rationalities? What is wrong with irrational values for a and r?

\(\displaystyle a_6 = a_1 r^5 = 64\\
a_{15} = a_1 r^{14} = 386\\
\dfrac{a_1 r^{14}}{a_1 r^5} = \dfrac{386}{64}=\dfrac{193}{32}\\
so \ r^9 = \dfrac{193}{32}\\
then \ r = (\dfrac{193}{32})^{1/9}\\
and \ a_1 =...
\)
 
UnlinkedNebula said:
Exactly, I got decimals every single time I tried so I thought I was doing something wrong …
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Hi UN. I was probably wrong to say earlier that your materials are probably wrong. It's just unusual to see a sequence exercise where all the elements are Irrational, seemingly, except for two. Now, there's nothing wrong with such a sequence; it's just kinda sneaky. I can't recall seeing such an exercise, before.

There are different ways to express the Irrational values of a1 and r exactly (versus using rounded, decimal approximations). We can use radical expressions or rational exponents (like Jomo did for r = [193/32][1/9], in post #9). The exact forms could be what's expected.

a1 ([193/32]^[1/9])5 = 64

Divide both sides by r5, to solve for a1

?
 
Jomo said:
I'm a bit confused, why does a and r be decimal or rationalities? What is wrong with irrational values for a and r?
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That's not what I was commenting on in post #8, if you're referring to me.

My concern is that since we haven't been told what answers were rejected, and being given correct decimal answers (in post #4) didn't trigger a response (such as thanks), maybe correct answers were tried and something went wrong. I'm just trying to elicit more information.
 
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