Write the first five terms of the arithmetic sequence defined recursively. $a _ { 1 } = \frac { 7 } { 8 } , a _ { n + 1 } = a _ { n } - \frac { 5 } { 8 }$

A) $\frac { 7 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 13 } { 8 }$
B) $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 13 } { 8 }$ , $\frac { 7 } { 8 }$
C) $\frac { 7 } { 8 }$ , $- \frac { 3 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 9 } { 4 }$ , -1
D) $\frac { 7 } { 8 }$ , $- \frac { 3 } { 8 }$ , $- \frac { 13 } { 8 }$ , -1, $\frac { 1 } { 4 }$
E) $\frac { 7 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 9 } { 4 }$

Question

Write the first five terms of the arithmetic sequence defined recursively.   $a _ { 1 } = \frac { 7 } { 8 } , a _ { n + 1 } = a _ { n } - \frac { 5 } { 8 }$  
 
A) $\frac { 7 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 13 } { 8 }$
B) $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 13 } { 8 }$ , $\frac { 7 } { 8 }$
C) $\frac { 7 } { 8 }$ , $- \frac { 3 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 9 } { 4 }$ , -1
D) $\frac { 7 } { 8 }$ , $- \frac { 3 } { 8 }$ , $- \frac { 13 } { 8 }$ , -1, $\frac { 1 } { 4 }$
E) $\frac { 7 } { 8 }$ , $\frac { 1 } { 4 }$ , $- \frac { 3 } { 8 }$ , -1, $- \frac { 9 } { 4 }$

Quizplus · Accepted Answer

The sequence starts with $a_1 = \frac{7}{8}$. Each subsequent term is found by subtracting $\frac{5}{8}$ from the previous term. So, $a_2 = \frac{7}{8} - \frac{5}{8} = \frac{2}{8} = \frac{1}{4}$, $a_3 = \frac{1}{4} - \frac{5}{8} = \frac{2}{8} - \frac{5}{8} = -\frac{3}{8}$, $a_4 = -\frac{3}{8} - \frac{5}{8} = -\frac{8}{8} = -1$, and $a_5 = -1 - \frac{5}{8} = -\frac{8}{8} - \frac{5}{8} = -\frac{13}{8}$.

Write the First Five Terms of the Arithmetic Sequence Defined a1=78,an+1=an−58a _ { 1 } = \frac { 7 } { 8 } , a _ { n + 1 } = a _ { n } - \frac { 5 } { 8 }a1​=87​,an+1​=an​−85​

Write the First Five Terms of the Arithmetic Sequence Defined $a _ { 1 } = \frac { 7 } { 8 } , a _ { n + 1 } = a _ { n } - \frac { 5 } { 8 }$