20 Answer: a₁ = 4
Step-by-step explanation:
\begin{lgathered}a_n=324,\ r=3,\ n=5\\\\a_n=a_1 \cdot r^{n-1}\\\\324=a_1\cdot 3^{5-1}\\\\\dfrac{324}{3^4}=a_1\\\\\dfrac{324}{81}=a_1\\\\\large\boxed{4}=a_1\end{lgathered}
a
n
=324, r=3, n=5
a
n
=a
1
⋅r
n−1
324=a
1
⋅3
5−1
3
4
324
=a
1
81
324
=a
1
4
=a
1
21 Answer: n = 13
Step-by-step explanation:
\begin{lgathered}a_n=\dfrac{1}{64},\ a_1=64,\ r=\dfrac{1}{2}\\\\a_n=a_1 \cdot r^{n-1}\\\\\dfrac{1}{64}=64\cdot \bigg(\dfrac{1}{2}\bigg)^{n-1}\\\\\dfrac{1}{64\cdot 64}=\bigg(\dfrac{1}{2}\bigg)^{n-1}\\\\\dfrac{1}{2^6\cdot 2^6}=\dfrac{1}{2^{n-1}}\\\\6+6=n-1\\\\\large\boxed{13}=n\end{lgathered}
a
n
=
64
1
, a
1
=64, r=
2
1
a
n
=a
1
⋅r
n−1
64
1
=64⋅(
2
1
)
n−1
64⋅64
1
=(
2
1
)
n−1
2
6
⋅2
6
1
=
2
n−1
1
6+6=n−1
13
=n
22 Answer: n = 5
Step-by-step explanation:
