Find the common difference of the arithmetic sequence $178,74,118,1,58,…\frac { 17 } { 8 } , \frac { 7 } { 4 } , \frac { 11 } { 8 } , 1 , \frac { 5 } { 8 } , \ldots$

A) $114\frac { 11 } { 4 }$
B) $\frac { 3 } { 8 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 7 } { 4 }$
E) $118\frac { 11 } { 8 }$

Question

Find the common difference of the arithmetic sequence   17 8 , 7 4 , 11 8 , 1 , 5 8 , … \frac { 17 } { 8 } , \frac { 7 } { 4 } , \frac { 11 } { 8 } , 1 , \frac { 5 } { 8 } , \ldots 8 17 ​ , 4 7 ​ , 8 11 ​ , 1 , 8 5 ​ , … A)    11 4 \frac { 11 } { 4 } 4 11 ​ B)    − 3 8 - \frac { 3 } { 8 } − 8 3 ​ C)    − 3 4 - \frac { 3 } { 4 } − 4 3 ​ D)    − 7 4 - \frac { 7 } { 4 } − 4 7 ​ E)    11 8 \frac { 11 } { 8 } 8 11 ​

James Williams · Accepted Answer

Final Answer : B, Explanation :   To find the common difference, subtract any term in the sequence from the term that follows it. For example,   7 4 − 17 8 = 14 − 17 8 = − 3 8 \frac{7}{4} - \frac{17}{8} = \frac{14 - 17}{8} = -\frac{3}{8} 4 7 ​ − 8 17 ​ = 8 14 − 17 ​ = − 8 3 ​  . This shows that the common difference is   − 3 8 -\frac{3}{8} − 8 3 ​  .

Find the common difference of the arithmetic sequence $178,74,118,1,58,…\frac { 17 } { 8 } , \frac { 7 } { 4 } , \frac { 11 } { 8 } , 1 , \frac { 5 } { 8 } , \ldots$

A) $114\frac { 11 } { 4 }$
B) $\frac { 3 } { 8 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 7 } { 4 }$
E) $118\frac { 11 } { 8 }$

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