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Help - what is the nth term for this sequence?

Dear TSR's mathematicians,

I recently encountered a GCSE-level sequences question, which I seem to be struggling with right now. While I am not exactly the most mathematically proficient student to have graced the planet (around 64% marks at GCSE), I still thought I could tackle this - apparently not!

What is the nth term for this sequence?

The sequence:
4, 7, 13, 25...

Thanks to anyone that can help/solve this!
:smile:
(edited 4 years ago)

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Original post by Tolgarda
Dear TSR's mathematicians,

I recently encountered a GCSE-level sequences question, which I seem to be struggling with right now. While I am not exactly the most mathematically proficient student to have graced the planet (around 64% marks at GCSE), I still thought I could tackle this - apparently not!

What is the nth term for this sequence?

The sequence:
4, 7, 13, 25...

Thanks to anyone that can help/solve this!
:smile:


Are you missing a term in between or is that the whole thing
Reply 2
All you do is just subtract 1 from each term and you should see what to do next.
Reply 3
Original post by Youssef Dahi
Are you missing a term in between or is that the whole thing


That's the whole thing.
Reply 4
Original post by Your Local Cat
All you do is just subtract 1 from each term and you should see what to do next.

I can't seem to find the nth term for that either. I think I have forgotten how to do that lol.
Reply 5
Original post by Tolgarda
Dear TSR's mathematicians,

I recently encountered a GCSE-level sequences question, which I seem to be struggling with right now. While I am not exactly the most mathematically proficient student to have graced the planet (around 64% marks at GCSE), I still thought I could tackle this - apparently not!

What is the nth term for this sequence?

The sequence:
4, 7, 13, 25...

Thanks to anyone that can help/solve this!
:smile:


u1=4,un=3(n1)+un1u_1 = 4, u_n = 3(n-1) + u_{n-1}. Use this.
Reply 6
Original post by esrever
u1=4,un=3(n1)+un1u_1 = 4, u_n = 3(n-1) + u_{n-1}. Use this.


I assume this is half of the problem? When I plug the numbers into the equation (e.g. n = 1 for the first term), the numbers just don't seem to add up. Sorry if this might seem absolutely obvious.
Reply 7
Original post by Tolgarda
I assume this is half of the problem? When I plug the numbers into the equation (e.g. n = 1 for the first term), the numbers just don't seem to add up. Sorry if this might seem absolutely obvious.


You can't plug in n = 1 into the equation. Equation is only valid for n > 1 where n is an integer.

To solve the problems fully, you should use something like this: un=3(n1)+un1=3(n1)+3(n2)+un2=...u_{n} = 3(n-1) + u_{n-1} = 3(n-1) + 3(n-2) + u_{n-2} = ....
Reply 8
Original post by esrever
You can't plug in n = 1 into the equation. Equation is only valid for n > 1 where n is an integer.

To solve the problems fully, you should use something like this: un=3(n1)+un1=3(n1)+3(n2)+un2=...u_{n} = 3(n-1) + u_{n-1} = 3(n-1) + 3(n-2) + u_{n-2} = ....


Damn, this seems slightly above GCSE level. I don't remember learning this at GCSE! Anyway, thank you for explaining this to me. :smile:

Also, how come the equation is only valid for n > 1 where n is an integer? I'm pretty curious aha. Is it because you already stated that u1=4u_1 = 4? Whenever I was practising sequences at GCSE, I would almost always plug 1 in first.
(edited 4 years ago)
Reply 9
Original post by Tolgarda
Damn, this seems slightly above GCSE level. I don't remember learning this at GCSE! Anyway, thank you for explaining this to me. :smile:

Also, how come the equation is only valid for n > 1 where n is an integer? I'm pretty curious aha. Is it because you already stated that u1=4u_1 = 4? Whenever I was practising sequences at GCSE, I would almost always plug 1 in first.


If u_1 = 4 is not given, then can you find the value of u_1, u_2, u_3 etc?
Reply 10
Original post by esrever
If u_1 = 4 is not given, then can you find the value of u_1, u_2, u_3 etc?

I thought that u1u_1 could be any number that begins the sequence, which is always given. I just plug 1 into the equation to see if it fits the first term. If it fits the first term, I try it with the second, and the third, and the fourth et cetera. Once I am confident that an equation for the nth term fits a certain number of terms in the sequence, I have the confidence to believe that it is correct.
(edited 4 years ago)
Original post by Tolgarda
I thought that u1u_1 could be any number that begins the sequence, which is always given. I just plug 1 into the equation to see if it fits the first term. If it fits the first term, I try it with the second, and the third, and the fourth et cetera.


Yes that's correct. But if it's given that u_1 = 4, then plugging n = 1 may not always be useful. In this case, plugging n = 1 gives you u_1 = u_0.
Reply 12
Original post by esrever
Yes that's correct. But if it's given that u_1 = 4, then plugging n = 1 may not always be useful. In this case, plugging n = 1 gives you u_1 = u_0.

I see.
yourlocalcat in post #3 had the correct idea

in the current GCSE spec, students are expected to know more sequence types than just linear ones.

linear sequences are still common, but there's now usually a quad sequence question on one of the papers, too.

other sequence types to be covered are:
Fibonacci
& other simple term to term

nth term sequences:
simple geometric sequences, involving powers of 2 or 3 (perhaps also 1/2 or 1/3)

hth
Reply 14
Original post by begbie68
yourlocalcat in post #3 had the correct idea

in the current GCSE spec, students are expected to know more sequence types than just linear ones.

linear sequences are still common, but there's now usually a quad sequence question on one of the papers, too.

other sequence types to be covered are:
Fibonacci
& other simple term to term

nth term sequences:
simple geometric sequences, involving powers of 2 or 3 (perhaps also 1/2 or 1/3)

hth

I did do the current GCSE spec lol.
lol just times 2 and -1 from the last term looooooooooooool
this is just a regular IQ test question on sequence

4 7 13 25 49. done


iq test is really, not mathematics. this is to be solved intuitively and quickly, not in a mathematical way like constructing Un and Un+1 term. if you get to solve an iq test question in that way, you prob get 60iq for missing over half of the questions
(edited 4 years ago)
or precisely ZERO marks for this question which is in BOLD in the first post :

what is the nth term for this sequence

Original post by ewoirjapwfjap
this is just a regular IQ test question on sequence

4 7 13 25 49. done


iq test is really, not mathematics. this is to be solved intuitively and quickly, not in a mathematical way like constructing Un and Un+1 term. if you get to solve an iq test question in that way, you prob get 60iq for missing over half of the questions
this sequence could ALSO be the start of either of these :

A229439
or
A039694
...
(edited 4 years ago)

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