An arithmetic sequence has u1 = 1/3 and u8 = 26. Find the common difference d.

Step-by-step solution

1. 1

   Write the eighth term with the nth-term rule. $u_8=u_1+(8-1)d=u_1+7d$ Only seven gaps separate $u_1$ from $u_8$, which is the step most often miscounted here.

2. 2

   Substitute the known values. $26=\frac{1}{3}+7d$

3. 3

   Isolate the $7d$ term over a common denominator. $7d=26-\frac{1}{3}=\frac{78-1}{3}=\frac{77}{3}$

4. 4

   Divide by 7. $d=\frac{77}{3}\cdot\frac{1}{7}=\frac{11}{3}$

5. 5

   Check by rebuilding $u_8$. $\frac13+7\cdot\frac{11}{3}=\frac{1+77}{3}=\frac{78}{3}=26$, which matches the data exactly, so the answer is A.