# in an algebraic arithmetic sequence, how do i find the missing number?

the question is: the first three terms of an arithmetic sequence are (12-p), 2p and (4p-5) respectively, where p is a constant. Find the value of p.

In an arithmetic sequence, you know that the difference between each consecutive term is the same. So in your case 2p-(12-p) is the same as (4p-5)-2p. You could build an equation with this fact, and then go on to solve for p.
ianmoth
07 January 2013
In an arithmetic sequence, you know that the difference between each consecutive term is the same. So in your case 2p-(12-p) is the same as (4p-5)-2p. You could build an equation with this fact, and then go on to solve for p.
ianmoth
07 January 2013
but what would they equal to, i'm completely stuck, i've tried to do a simultaneous equation but i dont think i've made the correct equations.
alicia96
07 January 2013
Thank you for helping
alicia96
07 January 2013
i've looked on student room and someone had the same problem and i've looked at that, but thank you for helping!#
alicia96
07 January 2013
2p-(12-p) = (4p-5)-2p
ianmoth
07 January 2013
got it!
alicia96
07 January 2013
In an arithmetic sequence, the difference between two consecutive terms is the same. For example, the following sequence has a common difference of 2: 1,3,5,7.... You could find this difference by subtracting any two of the consecutive terms. For example, 3-1=2, or 7-5=2. The sequence which you have is exactly the same except for the fact that it is written using letters for numbers. Since you know it is an arithmetic series, we know that the difference between two terms is always the same. Therefore, 2p-(12-p)=(4p-5)-2p. From there you should be able to rearrange to get an answer.
benlambert18785
10 January 2013