Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference.
-$$a _ { n } = \frac { 7 n - 1 } { 8 }$$
A) yes, $- \frac { 1 } { 8 }$
B) yes, 7
C) yes, $\frac { 7 } { 8 }$
D) no

Question

Quizplus · Accepted Answer

An arithmetic sequence has a constant difference between each term. To find if the given sequence is arithmetic, we can calculate the difference between consecutive terms. For $a_n = \frac{7n - 1}{8}$, the first term $a_1 = \frac{7(1) - 1}{8} = \frac{6}{8} = \frac{3}{4}$ and the second term $a_2 = \frac{7(2) - 1}{8} = \frac{13}{8}$. The difference between the second and the first term is $\frac{13}{8} - \frac{3}{4} = \frac{13}{8} - \frac{6}{8} = \frac{7}{8}$. This difference remains constant for any two consecutive terms, indicating the sequence is arithmetic with a common difference of $\frac{7}{8}$.

Determine If the Sequence Is Arithmetic an=7n−18a _ { n } = \frac { 7 n - 1 } { 8 }an​=87n−1​

Determine If the Sequence Is Arithmetic $a _ { n } = \frac { 7 n - 1 } { 8 }$