Use the Formula for the General Term of a Geometric SequenceUse the formula for the general term (the nth term)of a geometric sequence to find the indicated term of the
sequence with the given first term, $$\mathbf { a } _ { 1 }$$ , and common ratio, r.
-Find $a _ { 4 }$ when $a _ { 1 } = 2000 , r = - \frac { 1 } { 2 }$.
A) $- 250$
B) $- 125$
C) 250
D) $- 25$

Question

Quizplus · Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$. For $a_4$, $n = 4$, $a_1 = 2000$, and $r = -\frac{1}{2}$, so $a_4 = 2000 \cdot (-\frac{1}{2})^{(4-1)} = 2000 \cdot (-\frac{1}{2})^3 = 2000 \cdot -\frac{1}{8} = -250$.

Use the Formula for the General Term of a Geometric a1\mathbf { a } _ { 1 }a1​

Use the Formula for the General Term of a Geometric $\mathbf { a } _ { 1 }$