Question

Write an explicit formula for the sequence generated by a1 = 10, an = an − 1 + 7 where n = 2, 3, 4, .... (1 point)an = 7n − 10 where n = 1, 2, 3, ...an = 7n + 3 where n = 1, 2, 3, ...an = 3n + 4 where n = 1, 2, 3, ...an = n + 7 where n = 1, 2, 3, ...

Answer 1

Write an explicit formula for the sequence generated by a1 = 10, an = an − 1 + 7

`\begin{gathered} a_1=10 \\ a_n=a_(n-1)+7 \end{gathered}`

where n = 2, 3, 4,

n = 2

`\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}`

n = 3

`\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}`

n = 4

`\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}`

Therefore the explicit formular for the sequence will be

common difference

d = 31-24 = 24 - 17 = 7

`\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}`

Hence the correct answer is Option B