Find the nth term of the geometric sequence. $- 2 , - \frac { 5 } { 2 } , - \frac { 2.5 } { 8 } , \mathbf { K }$
A) $2 \left( - \frac { 5 } { 4 } \right) ^ { n - 1 }$
B) $2 \left( \frac { 5 } { 4 } \right) ^ { n - 1 }$
C) $- 2 \left( - \frac { 4 } { 5 } \right) ^ { n - 1 }$
D) $- 2 \left( \frac { 5 } { 4 } \right) ^ { n - 1 }$
E) $2 \left( - \frac { 4 } { 5 } \right) ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The common ratio (r) can be found by dividing any term in the sequence by its preceding term, e.g., $-\frac{5}{2} / -2 = \frac{5}{4}$. The first term (a) is $-2$. Thus, the nth term formula for a geometric sequence is $a \cdot r^{n-1}$, which gives $-2 \left( \frac{5}{4} \right)^{n-1}$.

Find the Nth Term of the Geometric Sequence −2,−52,−2.58,K- 2 , - \frac { 5 } { 2 } , - \frac { 2.5 } { 8 } , \mathbf { K }−2,−25​,−82.5​,K

Find the Nth Term of the Geometric Sequence $- 2 , - \frac { 5 } { 2 } , - \frac { 2.5 } { 8 } , \mathbf { K }$