Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) $$a _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }$$
A) $a _ { n } = - 7 n ; - 7 , - 21 , - 63 , - 189 , - 567$
B) $$a _ { n } = - 7 ( 3 ) ^ { n } ; - 21 , - 63 , - 189 , - 567 , - 1701$$
C) $a _ { n } = ( - 21 ) ^ { n } ; - 7 , - 63 , - 189 , - 567 , - 1701$
D) $a _ { n } = ( - 21 ) ^ { n - 1 } ; - 21 , - 63 , - 189 , - 567 , - 1701$
E) $a _ { n } = - 7 ( 3 ) ^ { n - 1 } ; - 7 , - 21 , - 63 , - 189 , - 567$

Question

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1. ) $$a _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }$$
A) $a _ { n } = - 7 n ; - 7 , - 21 , - 63 , - 189 , - 567$ ​
B) $$a _ { n } = - 7 ( 3 ) ^ { n } ; - 21 , - 63 , - 189 , - 567 , - 1701$$ ​
C) $a _ { n } = ( - 21 ) ^ { n } ; - 7 , - 63 , - 189 , - 567 , - 1701$ ​
D) $a _ { n } = ( - 21 ) ^ { n - 1 } ; - 21 , - 63 , - 189 , - 567 , - 1701$ ​
E) $a _ { n } = - 7 ( 3 ) ^ { n - 1 } ; - 7 , - 21 , - 63 , - 189 , - 567$ ​

Quizplus · Accepted Answer

The sequence starts with $a_1 = -7$, and each subsequent term is 3 times the previous term ($a_{k+1} = 3a_k$). This pattern matches option E, where the nth term is given by $a_n = -7(3)^{n-1}$, correctly generating the sequence $-7, -21, -63, -189, -567$.

Write the First Five Terms of the Sequence Defined Recursively a1=−7,ak+1=3aka _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }a1​=−7,ak+1​=3ak​

Write the First Five Terms of the Sequence Defined Recursively $a _ { 1 } = - 7 , a _ { k + 1 } = 3 a _ { k }$