let x, 8, y, z be an arithmetic sequence. if x, 8, z are geometric sequences, then the value of x + y + z is
1. let x, 8, y, z be an arithmetic sequence. if x, 8, z are geometric sequences, then the value of x + y + z is
Jawab:
Penjelasan dengan langkah-langkah:
x, 8, y, z → barisan aritmatika
U1 = x
U2 = 8
U3 = y
U4 = z
U1 + U3 = 2 . U2
x + y = 2 . 8
x + y = 16
y = 16 - x
U2 + U4 = 2 . U3
8 + z = 2y
8 + z = 2 . (16 - x)
8 + z = 32 - 2x
z = 32 - 2x - 8
z = 24 - 2x
x, 8, z → deret geometri
U1 = x
U2 = 8
U3 = z
U1 . U3 = (U2)²
x . z = 8²
x . z = 64
x . (24 - 2x) = 64
24x - 2x² = 64
2x² - 24x + 64 = 0
semua dibagi 2
x² - 12x + 32 = 0
(x - 4) . (x - 8) = 0
x - 4 = 0
x = 4 (memenuhi)
x - 8 = 0
x = 8 (tidak memenuhi karena U1 ≠ U2)
y = 16 - x
y = 16 - 4
y = 12
z = 24 - 2x
z = 24 - 2 . 4
z = 24 - 8
z = 16
x, 8, y, z
4, 8, 12, 16
x + y + z
= 4 + 12 + 16
= 32
Detail Jawaban
Kelas 9
Mapel 2 - Matematika
Bab 2 - Barisan dan Deret Bilangan
Kode Kategorisasi : 9.2.2
2. 2.Let x, 8, y, z be an arithmetic sequence. If x, 8, z are geometricsequences, then the value of x + y + z is...Please Helpp...
aritmatic x, 8, y, z
8 - x = y - 8
y + x = 8 + 8
x + y = 16
geometric x, 8, y
8 : x = y : 8
xy = 64
x = 64 : y
x + y = 16
(64 : y) + y = 16
(64 : y) + (y² : y) = 16
(64 + y²) = 16y
y² - 16y + 64 = 0
(y - 8)(y - 8) = 0
y = 8
x = 16 - 8 = 8
beda 8 - 8 = 0
maka x + y + z = 8 + 8 + 8 = 24
3. the 1st term of arithmatic sequences is 6 and 5th term ia 18 find the value of the difergen of the arithmatic sequences
Jawaban:
3
Penjelasan:
Un= a+(n-1)b
U1 = a = 6
U5= a+(n-1)b
18= 6+(5-1)b
18= 6+ 4b
18-6= 4b
12= 4b
b=3
so, the divergen of the arithmetic sequence is 3
4. 2. Let x, y and z are the first three terms of geometric sequence. Which of the following equation is true? A) xy = z B) xz = y C) x^2 = yz D) y^2 = xz E) z^2 = xy please use method, thank you
R = U2/U1 = U3/U2
= y/x = z/y
Y² = xz (D)
5. Write down the missing terms of this sequences. ? , 8 , 14 , ? , ? , 32 , 38 , ...
Jawaban:
2,8,14,20,26,32,38,44
6. Find a formula for the general term of each of the following sequences: a). 5, 9, 13, 17, 21... b). 7, 12, 17, 22, 27... Dengan caranya juga ya :)
Jawaban:
a..
a=5
b=9 - 5=4..
Un=a+(n-1)b
Un=5+(n-1)4
Un=5+4n-4
Un=4n+1..
b..
a=7
b=12-7=5
Un=a+(n-1)b
Un=7+(n-1)5
Un=7+5n-5
Un=5n+2..
7. A geometric sequence has 9 terms. If the third term is 80 and the last term is 327680, find the common ratio of the geometric sequence.
[tex]u9 = u3 \times {r}^{6} \\ 327680 = 80 \times {r}^{6} \\ \frac{327680}{80} = {r}^{6} \\ {r}^{6} = 4096 \\ r = \sqrt[6]{4096} \\ r = 4[/tex]
8. the second paragraph tell us about the ..... of the film. it tells the sequences of the ..... film in brief. this part of the text is called ......
Jawaban:
1. The plot of the film
2. The whole of film in brief.
3. Recount text (ada tercantum di dalam kotak)
Penjelasan:
9. b) Diberi suatu janjang geometri terbentuk daripada tiga nombor positif dengan r> 1. Jika sebutan kedua janjang geometri tersebut digandakan, jujukan nombor yang baru akan membentuk suatu janjang aritmetik. Cari nisbah sepunya bagi janjang geometri tersebut. Given a geometric progression is formed by three positive numbers which r> 1. If the second term of the geometric progression is doubled, the new numbers form an arithmetic progression. Find the common ratio of the geometric progression.
Penjelasan dengan langkah-langkah:
Let the three terms of the geometric progression be a, ar, and ar^2, where r > 1. The second term is ar, and if it is doubled, the three terms of the new arithmetic progression are a, 2ar, and ar^2.
Since the three terms form an arithmetic progression, we have:
2ar - a = ar^2 - 2ar
Simplifying this equation, we get:
3ar = ar^2 + a
3r = r^2 + 1
r^2 - 3r + 1 = 0
Solving for r using the quadratic formula, we get:
r = (3 ± sqrt(5))/2
Since r > 1, we take the positive root:
r = (3 + sqrt(5))/2
Therefore, the common ratio of the geometric progression is (3 + sqrt(5))/2.
10. The sum of the first four terms in a geometricsequence is 30 and the sum to infinity is 32. The firstthree terms of the sequence are ....
Jawaban:
Jumlah dari empat suku pertama dalam geometri
urutannya adalah 30 dan jumlah hingga tak terhingga adalah 32. Yang pertama
tiga suku urutan tersebut adalah ....
11. Which sequence isn't a geometric progression? Jawaban:3,6,9,12
Jawaban:
3,6,9,12 is not a geometric progression, it is a arithmetic progression with common diference = 3
12. if 6,a,b,c 96 geometric sequences, find a value B
Penjelasan dengan langkah-langkah:
r = rasio
6r⁴ = 96
r⁴ = 16
r = 2
6, 12, 24
b = 24
13. Give your own example of a geometric sequence with any of the following a.) an increasing geometric sequence b.) a decreasing geometric sequence c.) a geometric sequence where common ratio is between 0 and 1 d.) a geometric sequence where common ratio is negative Then, give the sum of your example using, 1.) the first four terms 2.) the first ten terms 3.) the first 100 terms
d.) a geometric sequence where common ratio is negative
14. Geometric Series&Sequences 1. Find U4,S4 & S∞ for the series below. 144 + 48 + 16 + ... 2. For a geometric sequence with u3 = 24 and u6 = 3, find S∞. 3. A geometric series has a common ratio of 0.4 and a sum to infinity of 250. Find the first term.
Jawaban:
mohon maaf saya tidak bisa menjawab soal kamu mohon maaf???
15. the text that tell someine's past experiences written in the sequences of events is a text of
that text called past simple
16. What is the meaning of the sequences?
Jawaban: a particular order in which related events, movements, or things follow each other.
17. the text that tell someine's past experiences written in the sequences of events is a text of
Jawaban:
Teks Cerita Ulang atau bisa juga disebut Rekon (bahasa Inggris: Recount) adalah Teks yang menceritakan suatu peristiwa atau kejadian atau kegiatan yang telah dilakukan/dialami.
Penjelasan:
Maaf klo salah ya.
18. C. If (x - 1), x, (x + 3) are the first 3 terms of a geometric sequence, find the value of x.
Lu indo atau inggris
19. the first three terms in geometric progression are (7x-7),(2x + 1),and (x-3) where x is a positive integer.find the value of x and find the sum of the first 5 terms of the progression
Kelas 8 Matematika
Bab Barisan dan Deret Bilangan
U1 = 7x - 7
U2 = 2x + 1
U3 = x - 3
(U2)² = U1 . U3
(2x + 1)² = (7x - 7) (x - 3)
4x² + 2 . 2x + 1 + 1² = 7x² - 21x - 7x + 21
4x² + 4x + 1 = 7x² - 28x + 21
7x² - 4x² - 28x - 4x + 21 - 1 = 0
3x² - 32x + 20 = 0
(3x - 2) (x - 10) = 0
3x - 2 = 0
3x = 2
x = 2/3
x - 10 = 0
x = 10
x = 10
U1 = 7x - 7
U1 = 7 . 10 - 7
U1 = 63 → a
U2 = 2x + 1
U2 = 2 . 10 + 1
U2 = 21
U3 = x - 3
U3 = 10 - 3
U3 = 7
r = U2 / U1
r = 21 / 63
r = 1/3
Sn = a . (1 - r^n)/(1 - r)
S5 = 63 . (1 - (1/3)^5)/(3/3 - 1/3)
S5 = 63 . (243/243 - 1/243) / (2/3)
S5 = 63 . 242/243 . 3/2
S5 = 7 . 121 /9
S5 = 847/9
S5 = 94 1/9
20. at is the meaning of sequences?A. The introduction of charactersB. The endding of the storyC. The series of eventD. The conclution of the storyE. Moral messege of the story
Jawaban:
The endding of the story
Penjelasan:
The endding of the story -›Atisthemeaningofsequances"Theendingofthestory"
Mapel:bahasaInggris
kode:-
0 Comments:
Post a Comment