Find the indicated term of the sequence.
-If the second term of a geometric progression is $\frac { 14 } { 5 }$ and the third term is $- \frac { 28 } { 5 }$, find a 1 and $\mathrm { r }$.
A) $a _ { 1 } = \frac { 56 } { 5 } ; r = - 2$
B) $a _ { 1 } = - \frac { 7 } { 5 } ; r = - \frac { 1 } { 2 }$
C) $a _ { 1 } = - \frac { 7 } { 5 } ; r = - 2$
D) $a _ { 1 } = - 7 ; r = - \frac { 2 } { 5 }$

Question

Quizplus · Accepted Answer

The second term of a geometric progression is given by $a_2 = a_1 * r$, where $a_1$ is the first term and $r$ is the common ratio. The third term is given by $a_3 = a_1 * r^2$.We are given that $a_2 = \frac{14}{5}$ and $a_3 = -\frac{28}{5}$. Substituting these values into the equations above, we get:$$\frac{14}{5} = a_1 * r$$$$-\frac{28}{5} = a_1 * r^2$$Dividing the second equation by the first equation, we get:$$r = -2$$Substituting this value of $r$ into the first equation, we get:$$a_1 = \frac{14}{5} * (-2) = -\frac{28}{5}$$Therefore, the first term is $a_1 = -\frac{28}{5}$ and the common ratio is $r = -2$.

Find the Indicated Term of the Sequence 145\frac { 14 } { 5 }514​

Find the Indicated Term of the Sequence $\frac { 14 } { 5 }$