1. Arithmetic Sequence Question

I am in Pure 20 (Pre-Calculus 11) and I am stumped on how to do this.

"The terms 5x + 2, 7x + 4, and 10x + 6 are consecutive terms of an arithmetic sequence. Determine the value of x and state the 3 terms."

The formula we have been using in all of the previous questions is
t-sub-n = t-sub-1 + (n-1)(d)
Where Tn = nth term, n = number of terms, T1 = first term, and d = common difference.

2. Re: Arithmetic Sequence Question

Well, you are given three consectutive values which must correspond to n-1, n, and n+1. Put those into your formula and you have three equations to solve for the three unknown numbers, $t_1$, d, and n.

But more fundamental and simpler, I think, for this question is that the difference between two consecutive terms is a constant- that is your "d". If three consecutive terms are 5x + 2, 7x + 4, and 10x + 6, the difference of the first two must equal the difference of the last two: [7x+ 4 - (5x+ 2)]= [(10x+ 5)- (7x+ 4)]. Solve that equation for x.