Find the indicated term of the sequence.
-The sixth term of the geometric sequence 4, 20, 100, ...
A) 3125
B) 100
C) 12,500
D) 62,500

Question

Quizplus · Accepted Answer

The sequence is a geometric sequence where each term is multiplied by 5 to get the next term (20/4 = 100/20 = 5). The sixth term can be found by multiplying the fifth term by 5. The fifth term is 100 * 5 = 500 (fourth term is 100), so the sixth term is 500 * 5 = 2,500. However, there seems to be a mistake in my calculation. Correctly, starting from the first term (4), to get the sixth term, we use the formula for the nth term of a geometric sequence: $a_n = a_1 \cdot r^{(n-1)}$, where $a_1 = 4$, $r = 5$, and $n = 6$. Thus, $a_6 = 4 \cdot 5^{(6-1)} = 4 \cdot 5^5 = 4 \cdot 3125 = 12,500$.

Find the Indicated Term of the Sequence