Math CentralQuandaries & Queries


Question from Dalal:

If x+1 and -x+17 are the second and sixth term of a sequence with a common difference of 5, what's the value of x.

I put it into an algebra equation but I didn't know what to do with the difference of 5.
Like x+1=2 and -x+17=6
Was that correct? Do I divide the answers by 5?

Hi Dalal,

In an arithmetic sequence the difference between any two successive terms is same regardless of which two successive terms you choose. This difference is called the common difference and often designated $d.$ Hence if the second term is $T$ then the third term is $T + d.$ Now that you know the third term you know that the fourth term is $(T + d) + d = T+2d.$ What is the fifth term? What is the sixth term?

In your problem the second term is $x + 1.$ According to the paragraph above what is the sixth term? But you know that the sixth term is $-x + 17.$ Solve for $x.$

Make sure you verify your answer.


Dalal wrote back

Hi I already asked this question but did not understand the reply, i dont understand how i would find the value of x

In your problem the second term is $x+1$ so the third term is $(x+1) + d,$ the fourth term is $(x+1) +d +d,$ the fifth term is $(x+1) + d + d + d$ and the sixth term is $(x+1) + d + d + d + d.$ But you know that $d = 5$ so the sixth term is $(x + 1) + 20 = x + 21.$ Hence $x+21 = -x + 17.$ Solve for x.


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