Find the indicated nth term of the geometric sequence. $$10 \text { th term: } 2 , - 10,50 , \ldots$$
A)-5,120
B)-3,906,250
C)-2,560
D)-43
E)19,531,250

Question

Quizplus · Accepted Answer

The common ratio (r) can be found by dividing the second term by the first term: r = -10 / 2 = -5. The nth term of a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number. Here, $a_1 = 2$, $r = -5$, and $n = 10$. Thus, the 10th term is $2 \cdot (-5)^{10-1} = 2 \cdot (-5)^9 = 2 \cdot -1,953,125 = -3,906,250$.

Find the Indicated Nth Term of the Geometric Sequence 10 th term: 2,−10,50,…10 \text { th term: } 2 , - 10,50 , \ldots10 th term: 2,−10,50,…

Find the Indicated Nth Term of the Geometric Sequence $10 \text { th term: } 2 , - 10,50 , \ldots$