Find the first term and the common difference.
-$$\frac { 7 } { 12 } , \frac { 1 } { 3 } , \frac { 1 } { 12 } , - \frac { 1 } { 6 } , \ldots$$
A) $\mathrm { a } _ { 1 } = \frac { 7 } { 12 } , \mathrm {~d} = \frac { 1 } { 4 }$
B) $\mathrm { a } _ { 1 } = \frac { 7 } { 12 } , \mathrm {~d} = - \frac { 1 } { 4 }$
C) $a _ { 1 } = \frac { 7 } { 12 } , \mathrm {~d} = \frac { 7 } { 12 }$
D) $\mathrm { a } _ { 1 } = \frac { 7 } { 12 } , \mathrm {~d} = - \frac { 3 } { 4 }$

Question

Quizplus · Accepted Answer

The first term $a_1$ is clearly $\frac{7}{12}$ as given in the sequence. To find the common difference $d$, subtract the first term from the second term: $\frac{1}{3} - \frac{7}{12} = -\frac{1}{4}$. This pattern of subtracting $\frac{1}{4}$ continues with each subsequent term, confirming the common difference is $-\frac{1}{4}$.

Find the First Term and the Common Difference 712,13,112,−16,…\frac { 7 } { 12 } , \frac { 1 } { 3 } , \frac { 1 } { 12 } , - \frac { 1 } { 6 } , \ldots127​,31​,121​,−61​,…

Find the First Term and the Common Difference $\frac { 7 } { 12 } , \frac { 1 } { 3 } , \frac { 1 } { 12 } , - \frac { 1 } { 6 } , \ldots$