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An arithmetic sequence is defined by the recursive formula t1 = 44, tn + 1 = tn + 16, where n ∈N and n ≥ 1. Which is the general term of the sequence? A) tn = 44 + (n - 1)16, where n ∈N and n ≥ 1 B) tn = 44 + (n + 1)16, where n ∈N and n ≥ 1 C) tn = 44 + (n - 2)16, where n ∈N and n ≥ 1 D) tn + 1 = 44 + (n - 1)16, where n ∈N and n ≥ 0

User Henfs
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1 Answer

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\begin{cases}t_1=44\\t_(n+1)=t_n+16&\text{for }n>1\end{cases}

According to this rule, we get


t_2=t_1+16


t_3=t_2+16=t_1+2\cdot16


t_4=t_3+16=t_1+3\cdot16

and so on, up to


t_n=t_(n-1)+16=t_(n-2)+2\cdot16=\cdots


\implies t_n=t_1+(n-1)\cdot16

Then


t_n=44+16(n-1)=16n+28

which matches answer A.

User Mihai Neacsu
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9.5k points
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