An arithmetic sequence satisfies u4 = 10 and u4 + u6 = 26. Find the common difference d.

Step-by-step solution

1. 1

   Use the first equation to peel off $u_6$. Substituting $u_4=10$ into $u_4+u_6=26$ gives $u_6=26-10=16$

2. 2

   Relate two terms directly. Instead of introducing $u_1$, use $u_m-u_n=(m-n)d$: $u_6-u_4=(6-4)d=2d$

3. 3

   Solve for $d$. $2d=16-10=6\quad\Longrightarrow\quad d=3$

4. 4

   Recover the first term as a check. $u_4=u_1+3d=u_1+9=10$, so $u_1=1$ and the sequence is $1,4,7,10,13,16,\dots$

5. 5

   Confirm both conditions. With that sequence $u_4=10$ and $u_4+u_6=10+16=26$, both satisfied, so the answer is B, $d=3$.