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.

Penny

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.

Penny