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.
-$$a _ { n } = 3 ^ { n }$$
A) geometric, $r = 3$
B) arithmetic, $\mathrm { d } = 3$
C) geometric, $r = 4$
D) neither

Question

Quizplus · Accepted Answer

The formula for the general term of a geometric sequence is: $$a_n = a_1 \cdot r^{n-1}$$ 
Comparing this formula with the given sequence, we can see that:
$$a_1 = 3^{1} = 3$$ 
$$r = 3$$
So, the formula becomes:
$$a_n = 3 \cdot 3^{n-1} = 3^n$$
which matches the given sequence. Therefore, this is a geometric sequence with common ratio r = 3.

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 $\mathbf { a } _ { 1 }$