# 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.

Answers

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.

07 January 2013

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.

07 January 2013

Thank you for helping

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!#

07 January 2013

2p-(12-p) = (4p-5)-2p

07 January 2013

got it!

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.

10 January 2013

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