Given are the first three terms of a sequence that is either arithmetic or geometric. If the sequence is arithmetic, find a1
and d. If a sequence is geometric, find a1 and r.
-$\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \ldots$
A) $a _ { 1 } = \frac { 3 } { 4 } , r = 4$
B) $a _ { 1 } = \frac { 3 } { 4 } , r = 40$
C) $\mathrm { a } _ { 1 } = \frac { 3 } { 4 } , \mathrm { r } = \frac { 1 } { 40 }$
D) $\mathrm { a } _ { 1 } = \frac { 3 } { 4 } , \mathrm { r } = \frac { 1 } { 4 }$

Question

Quizplus · Accepted Answer

The sequence is geometric because each term is obtained by multiplying the previous term by a constant ratio. The first term $a_1 = \frac{3}{4}$, and the ratio $r$ can be found by dividing the second term by the first term: $r = \frac{\frac{3}{16}}{\frac{3}{4}} = \frac{1}{4}$.

Given Are the First Three Terms of a Sequence That 34,316,364,…\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \ldots43​,163​,643​,…

Given Are the First Three Terms of a Sequence That $\frac { 3 } { 4 } , \frac { 3 } { 16 } , \frac { 3 } { 64 } , \ldots$