basic sequences question

Question

I'm just wondering about the following and cannot work it out;

Yoko is making a sequence, with each stage made up of a certain number of Xs arranged in a pattern. In Yoko’s sequence, the relationship between N and S is given by the formula: $N = 1+2S$

where N is the number of Xs in stage S of the sequence (starting at stage $0$).

The question is p represents the number of Xs in stage y of Yoko's sequence. Write down the number of Xs in stage $y+3$ of Yoko's sequence. Give your answer in terms of p.

Now the answer given is $p+6$ and I cannot seem to figure out why. Firstly, if I am giving an answer 'in terms' of p, should my answer not be '$p = ...?'

Secondly, I thought the answer would be $p = 2y +7$ because it reads to me as if we are just changing variables between p and N, and S and y (and y+3 after?)

Can anyone explain why the answer is $p +6$?

Thanks

Answer 1

By definition $p=1+2y$, and three stages later the amount of $X$'s is $1+2(y+3)$. That's $p+6$.