12 Answer: 20.25
Explanation:
\begin{lgathered}a_1=4,\ r=1.5,\ n=5\\\\a_n=a_1\cdot r^{n-1}\\\\a_5=4\cdot (1.5)^{5-1}\\\\.\ =4\cdot (1.5)^4\\\\.\ =4\cdot 5.0625\\\\.\ =\large\boxed{20.25}\end{lgathered}
a
1
=4, r=1.5, n=5
a
n
=a
1
⋅r
n−1
a
5
=4⋅(1.5)
5−1
. =4⋅(1.5)
4
. =4⋅5.0625
. =
20.25
13 Answer: 1980
Explanation:
16 Answer: 12
Explanation:
\begin{lgathered}\sum\limits^\infty_{n=1} 6\bigg(\dfrac{1}{2}\bigg)^{n-1}\\\\\\S_1=6\qquad \qquad S_2=3\qquad \qquad S_3=1.5\\\\\\\sum\limits^\infty_{n=1} 6\bigg(\dfrac{2}{2^n}\bigg)=\sum\limits^\infty_{n=1} 6\cdot 2\bigg(\dfrac{1}{2^n}\bigg)=12+\sum\limits^\infty_{n=1}\bigg(\dfrac{1}{2^n}\bigg)=12+0=\large\boxed{12}\end{lgathered}
n=1
∑
∞
6(
2
1
)
n−1
S
1
=6S
2
=3S
3
=1.5
n=1
∑
∞
6(
2
n
2
)=
n=1
∑
∞
6⋅2(
2
n
1
)=12+
n=1
∑
∞
(
2
n
1
)=12+0=
12