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nth term of a sequence....

[Edit]
(edited 12 years ago)
Reply 1
Avatar for Cerdog
Cerdog
Set n=2kn = 2k, and consider that −8=(−2)3-8 = (-2)^3. You should be able to make some progress from there (unless I've made a misunderstanding somewhere).
Reply 2
Avatar for f1mad
f1mad
13
Yeah that sounds right.
Reply 3
Avatar for flown_muse
flown_muse
OP
15
[Edit]
(edited 12 years ago)
Reply 4
Avatar for Cerdog
Cerdog
Original post by flown_muse
Okay, now I have:

Unparseable latex formula:

a_2_k = \frac{(2k-1)(-2)^3^(^2^k^+^1^)}{2^(^2^k^-^1^)}



and now I have an issue, because I can't find a value of k that can make both the top and the bottom equal to a power of 4.

I'm clearly doing something wrong :frown:


Write it as
Unparseable latex formula:

a_2_k = (2k-1)\frac{(-2)^3^(^2^k^+^1^)}{2^(^2^k^-^1^)}

, and remember that −2=−1×2-2 = -1 \times 2, so you can expand the powers to get something easier.
Reply 5
Avatar for f1mad
f1mad
13
Original post by flown_muse
Okay, now I have:

Unparseable latex formula:

a_2_k = \frac{(2k-1)(-2)^3^(^2^k^+^1^)}{2^(^2^k^-^1^)}



and now I have an issue, because I can't find a value of k that can make both the top and the bottom equal to a power of 4.

I'm clearly doing something wrong :frown:


Expand the numerator and simplify.
Reply 6
Avatar for flown_muse
flown_muse
OP
15
[Edit]
(edited 12 years ago)
Reply 7
Avatar for f1mad
f1mad
13
Original post by flown_muse
Unparseable latex formula:

a_2_k = (2k-1)\frac{(-2)^3^(^2^k^+^1^)}{2^(^2^k^-^1^)}


Unparseable latex formula:

a_2_k = (2k-1)\frac{(-1)(2)^(^6^k^+^3^)}{2^(^2^k^-^1^)}


Unparseable latex formula:

a_2_k = (2k-1).(-1)(2)^(^6^k^+^3^)^-^(^2^k^-^1^)


Unparseable latex formula:

a_2_k = (2k-1).(-1)(2)^(^4^k^-^2^)



etc.?


What's 3--1?

Apart from that yeah that's right. You can get rid of the 1 btw.
(edited 12 years ago)
Reply 8
Avatar for flown_muse
flown_muse
OP
15
Original post by f1mad
Yeah that's right. You can get rid of the 1 btw.


So, I have ended up with:

Unparseable latex formula:

a_2_k = (2k-1).(-1)(2)^(^4^k^+^4^)


Unparseable latex formula:

a_2_k = (1-2k).2^4^k^+^4



Therefore, 4k+4=4,4k=0 4k+4=4, 4k=0
Reply 9
Avatar for f1mad
f1mad
13
Original post by flown_muse
So, I have ended up with:

Unparseable latex formula:

a_2_k = (2k-1).(-1)(2)^(^4^k^+^4^)


Unparseable latex formula:

a_2_k = (1-2k).2^4^k^+^4



Therefore, 4k+4=4,4k=0 4k+4=4, 4k=0


Hang on, where did the last line come from?
Reply 10
Avatar for flown_muse
flown_muse
OP
15
Original post by f1mad
Hang on, where did the last line come from?


Because the question wants me to find An in terms of powers of 4, so I'm setting the power equal to 4.

(I think?)
Reply 11
Avatar for flown_muse
flown_muse
OP
15
Oh. I never thought of that. I think you are right, because otherwise I end up with n=0 and the answer is just a number with no powers. Argh! Thanks :smile:
Reply 12
Avatar for f1mad
f1mad
13
Original post by flown_muse
Oh. I never thought of that. I think you are right, because otherwise I end up with n=0 and the answer is just a number with no powers. Argh! Thanks :smile:


Yeah you need to re-write it :tongue:. In terms of 4^ something, since this would then imply powers of 4.

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