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.) $a _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }$
A) $a _ { k } = ( 24 ) ^ { n } ; - 8 , - 512,4096 , - 32768,262144$
B) $a _ { n } = - 8 ( - 3 ) ^ { n - 1 } ; - 8,24 , - 72,216 , - 648$
C) $a _ { n } = - 8 n ; - 8 , - 16 , - 24 , - 32 , - 40$
D) $a _ { k } = ( 24 ) ^ { n - 1 } ; - 8 , - 512,4096 , - 32768,262144$
E) $a _ { n } = - 8 ( - 3 ) ^ { n } ; 24 , - 72,216 , - 648,1944$

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.) $a _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }$
A) $a _ { k } = ( 24 ) ^ { n } ; - 8 , - 512,4096 , - 32768,262144$  
B) $a _ { n } = - 8 ( - 3 ) ^ { n - 1 } ; - 8,24 , - 72,216 , - 648$  
C) $a _ { n } = - 8 n ; - 8 , - 16 , - 24 , - 32 , - 40$  
D) $a _ { k } = ( 24 ) ^ { n - 1 } ; - 8 , - 512,4096 , - 32768,262144$  
E) $a _ { n } = - 8 ( - 3 ) ^ { n } ; 24 , - 72,216 , - 648,1944$

Quizplus · Accepted Answer

The sequence is defined recursively with each term being -3 times the previous term, starting with -8. The first five terms are -8, 24, -72, 216, -648, which follows the pattern of multiplying by -3 each time. The nth term can be expressed as $a_n = -8(-3)^{n-1}$ because each term is -3 times the previous term, starting from -8 for the first term.

Write the First Five Terms of the Sequence Defined Recursively a1=−8,ak+1=−3aka _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }a1​=−8,ak+1​=−3ak​

Write the First Five Terms of the Sequence Defined Recursively $a _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }$