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GCSE Sequences Question, find two terms in both help !

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

(edited 2 years ago)

Reply 1

mqb2766

Original post by DarkTin123

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.

(edited 2 years ago)

Reply 2

DarkTin123

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

Reply 3

mqb2766

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, ...

Reply 4

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)

Reply 5

mqb2766

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.

Reply 6

Tacklemathsuk

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