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15 votes
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, ...

Write an explicit formula for the sequence generated by a1 = 10, an = an − 1 + 7 where-example-1
User Vaggelis Stefanakis
by
2.6k points

1 Answer

23 votes
23 votes

Solution

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

User Misterben
by
3.0k points
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