Write the first five terms of the sequence defined recursively.
-$$a _ { 1 } = 20 ; a _ { n } = \frac { 1 } { 4 } a _ { n - 1 } + 3$$
A) $a _ { 1 } = 20 , a _ { 2 } = \frac { 23 } { 4 } , a _ { 3 } = \frac { 13 } { 8 } , a _ { 4 } = \frac { 29 } { 64 } , a _ { 5 } = \frac { 1 } { 8 }$
B) $a _ { 1 } = 20 , a _ { 2 } = 23 , a _ { 3 } = 26 , a _ { 4 } = 29 , a _ { 5 } = 32$
C) $a _ { 1 } = 20 , a _ { 2 } = 5 , a _ { 3 } = \frac { 5 } { 4 } , a _ { 4 } = \frac { 5 } { 16 } , a _ { 5 } = \frac { 5 } { 64 }$
D) $a _ { 1 } = 20 , a _ { 2 } = 8 , a _ { 3 } = 5 , a _ { 4 } = \frac { 17 } { 4 } , a _ { 5 } = \frac { 65 } { 16 }$

Question

Quizplus · Accepted Answer

Given the recursive formula $a_n = \frac{1}{4}a_{n-1} + 3$, we calculate the first five terms as follows: $a_1 = 20$, $a_2 = \frac{1}{4}(20) + 3 = 8$, $a_3 = \frac{1}{4}(8) + 3 = 5$, $a_4 = \frac{1}{4}(5) + 3 = \frac{17}{4}$, $a_5 = \frac{1}{4}(\frac{17}{4}) + 3 = \frac{65}{16}$.

Write the First Five Terms of the Sequence Defined Recursively a1=20;an=14an−1+3a _ { 1 } = 20 ; a _ { n } = \frac { 1 } { 4 } a _ { n - 1 } + 3a1​=20;an​=41​an−1​+3

Write the First Five Terms of the Sequence Defined Recursively $a _ { 1 } = 20 ; a _ { n } = \frac { 1 } { 4 } a _ { n - 1 } + 3$