This document discusses geometric sequences and provides an example to calculate the total amount of money after 10 months. It shows that the general term of a geometric sequence is Un = arn-1 and uses this to derive the common ratio r = 3/2 from example terms. It then calculates the 10th term S10 using the geometric sequence formula to find the total amount after 10 months is 12,046,000.

1. BARIS DAN DERET GEOMETRI

3. Un = a. r n – 1
U2 = ar2 – 1 = ar1
U4 = ar4 – 1 = ar3
𝑈4
𝑈2
=
27
12
𝑎𝑟3
𝑎𝑟1 =
27
12
(perkecil dibagi 3)
𝑟3
𝑟1 =
9
4
r 3 – 1 =
9
4
r 2 =
9
4
r = √
9
4
r =
3
2
U2 = ar2 – 1 = ar1
12 = a . (
3
2
)
a =
12 𝑥 2
3
= 8
U3 = ar3 – 1 = ar2
U3 = 8 . (
3
2
)2 = 8 .
9
4
= 18

4. JAWAB :
Sn =
1
3
(3𝑛+2
− 9)
r =
𝑈2
𝑈1
U1 = S1
U2 = S2 - S1
S1 =
1
3
(31+2
− 9)
S1 =
1
3
(33
− 9)
S1 =
1
3
(27 − 9)
S1 =
1
3
(18)
U1 = S1 = 6
S2 =
1
3
(32+2
− 9)
S2 =
1
3
(34
− 9)
S2 =
1
3
(81 − 9)
S2 =
1
3
(72)
S2 = 24
U2 = S2 - S1 = 24 – 6 = 18
r =
𝑈2
𝑈1
=
18
6
= 2
JAWAB :
Keuntungan = 2.000, 4.000, 8.000, …..
r =
4.000
2.000
= 2
S10 ? total uang setelah 10 bulan ?
Sn =
𝑎 (𝑟𝑛
−1)
𝑟−1
, r > 1
S10 =
2.000 (210
−1)
2−1
S10 =
2.000 (1.024 − 1)
1
S10 =
2.000 (1.023)
1
S10 =
2.046 .000
1
= 2.046.000
total uang setelah 10 bulan = 10.000.000 + 2.046.000 = 12.046.000