Solution
Write an explicit formula for the sequence generated by a1 = 10, an = an − 1 + 7
[tex]\begin{gathered} a_1=10 \\ a_n=a_{n-1}+7 \end{gathered}[/tex]
where n = 2, 3, 4,
n = 2
[tex]\begin{gathered} T_n=a_{n-1}+7 \\ where\text{ n = 2} \\ a_n=a_{n-1}+7 \\ a_2=a_{2-1}+7 \\ a__2=a_1+7 \\ a_2=10+7 \\ a_2=17 \end{gathered}[/tex]
n = 3
[tex]\begin{gathered} T_n=a_{n-1}+7 \\ where\text{ n = 3} \\ a_n=a_{n-1}+7 \\ a_3=a_{3-1}+7 \\ a_3=a_2+7 \\ a_2=17+7 \\ a_2=24 \end{gathered}[/tex]
n = 4
[tex]\begin{gathered} T_n=a_{n-1}+7 \\ where\text{ n = 3} \\ a_n=a_{n-1}+7 \\ a_3=a_{3-1}+7 \\ a_3=a_2+7 \\ a_2=17+7 \\ a_2=24 \end{gathered}[/tex]
Therefore the explicit formular for the sequence will be
common difference
d = 31-24 = 24 - 17 = 7
[tex]\begin{gathered} T_n=a+(n-1)d \\ T_n=10+(n-1)7 \\ T_n=10+7n-7 \\ T_n=7n+3 \end{gathered}[/tex]
Hence the correct answer is Option B
