GCSE Sequences Question, find two terms in both help !

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#1
Here are the first four terms of a number sequence.

2 7 12 17

Here are the first five terms of another number sequence.

–4 –1 2 5 8

Find two numbers that are in both number sequences.

My Attempt : Nth term of sequence 1 is 5n-3
Nth term of sequence 2 is 3n -7.

3n-7 =5n -3
2n= -4
n=-2

Sub n= -2 into the two nth terms
we get -13. But -13 is not an acceptable answer
Last edited by DarkTin123; 4 days ago
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4 days ago
#2
(Original post by DarkTin123)
Here are the first four terms of a number sequence.

2 7 12 17

Here are the first five terms of another number sequence.

–4 –1 2 5 8

Find two numbers that are in both number sequences.

My Attempt : Nth term of sequence 1 is 5n-3
Nth term of sequence 2 is 3n -7.

3n-7 =5n -3
2n= -4
n=-2

Sub n= -2 into the two nth terms
we get -13. But -13 is not an acceptable answer
The value of the index n will not be the same in both sequences.
simply spot two values that occur in both. Its not too hard to work out a general solution but its not required.
Last edited by mqb2766; 4 days ago
1
#3
(Original post by mqb2766)
The value of the index n will not be the same in both sequences.
simply spot two values that occur in both. Its not too hard to work out a general solution but its not required.
Of course! What would a general solution be ? Instead of "n" being the same, it would be two different variables presumably
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4 days ago
#4
(Original post by DarkTin123)
Of course! What would a general solution be ? Instead of "n" being the same, it would be two different variables presumably
what two values did you get? whats the difference? can you guess the third, fourth value, ...
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#5
Yep, I just equated to two nth terms (with one in terms of n and another in terms of x) and then used inspection to guess some values (e.g. 2 and 17)
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4 days ago
#6
(Original post by DarkTin123)
Yep, I just equated to two nth terms (with one in terms of n and another in terms of x) and then used inspection to guess some values (e.g. 2 and 17)
2 is obvious as its given in the question, 17 is 15 = 3*5 greater than 2.
Its known as a chinese remainder theorem problem.
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4 days ago
#7
This question has mostly been answered now, but I'd re-iterate that any answers don't have the same place in the sequences so that is why your method doesn't work... It was inventive and I can see why you thought that.. unfortunately wrong

Once you know the gap in the sequences were n and m then a common answer will happen every n x m... I'll let you work out what that is for your sequences.... As someone has said you can see one number is in both sequences so that gives a startin gpoint
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