Use 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, a1, and common ratio, r.
-Find $a _ { 12 }$ when $a _ { 1 } = 2,000 , r = - \frac { 1 } { 3 }$
A) $- \frac { 2000 } { 1594323 }$

B) $\frac { 5989 } { 3 }$

C) $\frac { 2000 } { 531441 }$

D) $- \frac { 2000 } { 177147 }$

Question

Use 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, a1, and common ratio, r.
-Find $a _ { 12 }$ when $a _ { 1 } = 2,000 , r = - \frac { 1 } { 3 }$
A) $- \frac { 2000 } { 1594323 }$

B) $\frac { 5989 } { 3 }$

C) $\frac { 2000 } { 531441 }$

D) $- \frac { 2000 } { 177147 }$

Quizplus · Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$. Substituting $a_1 = 2000$, $r = -\frac{1}{3}$, and $n = 12$, we get $a_{12} = 2000 \cdot (-\frac{1}{3})^{11}$. Since $11$ is odd, the result will be negative, and $(-1/3)^{11} = -1/177147$, thus $a_{12} = -\frac{2000}{177147}$.

Use the Formula for the General Term (The Nth Term) a12a _ { 12 }a12​

Use the Formula for the General Term (The Nth Term) $a _ { 12 }$