1.suatu barisan geometri diketahui suku ke 2 dan ke 5 adalah 5/4 dan 10 suku ke 7 barisan tersebut adalah 2.tentukan jumlah suku ke 5 dari deret 600+300+100 3.s

1. barisan geometri
U2 = 5/4 => ar = 5/4
U5 = 10 => ar⁴ = 10

ar(r)³ = 10
5/4r³ = 10
r³ = 8
r = 2

ar = 5/4
2a = 5/4
a = ⅝

U7 = ar^6 = ⅝(2)^6 =⅝(64) = 40

2. 600+300+100
U2 = 600 - 300 = 300
U3 = 300 - 200 = 100
U4 = 100 - 100 = 0
U5 = 0-0 = 0
S5 = 300+100=400

3. deret geometri
U2 = 10 => ar=10
U6 = 160 => ar^5 = 160

(ar)r⁴ = 160
10r⁴ = 160
r⁴ = 16
r = 2

ar = 10
2a = 10
a = 5

Sn = a{ (r^n) - 1 / (r-1) }
S10 = 5{ (2^10) -1 / (2-1)}
S10 = 5(511) = 5115

4. deret geometri
U2 = 32 => ar = 32
U5 = 4 => ar⁴ = 4

(ar)r³ = 4
32r³ = 4
r³ = 1/8
r = 1/2

ar = 32
½a = 32
a = 64

S7 = 64 { (½^7) - 1 / (½ - 1)}
S7 = 64 (127/64)
S7 = 127

5. deret geometri
U3 = 36 => ar² = 36
U5 = 324 => ar⁴ = 324

(ar²)r² = 324
36r² = 324
r² = 9
r = 3

ar² = 36
9a = 36
a = 4

S6 = 4{ (3^6) - 1 / (3-1) }
S6 = 4(364)
S6 = 1456