An arithmetic sequence has first term u1 = 3 and common difference d = 2. Find u5.

Step-by-step solution

1. 1

   Recall the nth-term rule. Every arithmetic sequence satisfies $u_n=u_1+(n-1)d$ The factor is $n-1$, not $n$, because you take $d$ steps only between terms.

2. 2

   Identify the three inputs. Here $u_1=3$, $d=2$ and the target index is $n=5$, so there are $5-1=4$ steps of size $2$ from the first term.

3. 3

   Substitute. $u_5=3+(5-1)\cdot 2=3+8=11$

4. 4

   Verify by listing the terms. $u_1=3$, $u_2=5$, $u_3=7$, $u_4=9$, $u_5=11$ — the listed value matches the formula.

5. 5

   Watch the off-by-one trap. Using $u_1+nd=3+5(2)=13$ or the option $15$ (which is $u_7$) both come from miscounting the steps. The correct answer is A, $u_5=11$.