What is the value of first term and common ratio of the geometric sequence if the third term is 96 and the fifth term is 1,536?
1. What is the value of first term and common ratio of the geometric sequence if the third term is 96 and the fifth term is 1,536?
Jawaban:
cara dan jawabannya seperti di foto ya.
semangat belajar
semoga membantu
#terbaik5
2. 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]
3. I have a geometric series problem . please help me to solve it Problem: The third term of a geometric sequence is 3 and the sixth term is 1/9. Find the first term.
The 1st term is 27.
@wello1
☺
4. in arithmetic sequence, the sum of the first ten terms is 125 and the third term is 5. Find the first term, the common difference and the sum of the first 15 terms
Arithmetic Sequence
• The nth term (Un)
Un = a + (n - 1) b
• The sum of the first n terms (Sn)
Sn = n/2 × (a + Un)
Sn = n/2 × (2a + (n - 1) b)
a = the first term
b = the common difference
==================================
S₁₀ = 125
U₃ = 5
a = ?
b = ?
S₁₅ = ?
S₁₀ = 125
10/2 × (2a + (10 - 1) b) = 125
5 × (2a + 9b) = 125
2a + 9b = 25 ... eq (1)
U₃ = 5
a + (3 - 1) b = 5
a + 2b = 5 ... eq (2)
To find a and b, use the elimination/substitution
▪︎Find the first term
Eliminate variable b to find a
2a + 9b = 25 (×2)
a + 2b = 5 (×9)
4a + 18b = 50
9a + 18b = 45
___________ -
-5a = 5
a = -1
The first term is -1
▪︎Find the common difference
To find the common difference, substitute a = -1 to eq (2)
a + 2b = 5
-1 + 2b = 5
2b = 5 + 1
2b = 6
b = 3
The common difference is 3
▪︎Find the sum of the first 15 terms
S₁₅ = 15/2 × [2(-1) + (15 - 1)(3)]
S₁₅ = 15/2 × [-2 + (14)(3)]
S₁₅ = 15/2 × (-2 + 42)
S₁₅ = 15/2 × 40
S₁₅ = 15 × 20
S₁₅ = 300
The sum of the first 15 terms is 300.
Hope it helps.
5. find the sum of the terms of an infinite geometric sequence whose first term is 4 and common ratio ⅕
" Barisan Geometri "
__________
>>>Diketahui:
a = 4
r = ⅕
________
>>> S∞ = ....
___________
[tex] \sf S_{ \infty } = \frac{a}{1 - r} [/tex]
[tex] \sf S_{ \infty } = \frac{4}{1 - \frac{1}{5} } [/tex]
[tex] \sf S_{∞} = \frac{4}{ \frac{4}{5} } [/tex]
[tex] \sf\to 4 \div \frac{ 4}{5} \\ \sf \to \cancel{4} \times \frac{5}{ \cancel{4}} [/tex]
[tex] \boxed{ \sf S_{∞} = 5}[/tex]
____________
CMIIW
Ciyo.
6. Given the Tn of a sequence is Tn = 4n + 7. The 9th term of the sequence is .… *
Jawaban:
Write the correct answer!= T(9) = 4(9) + 7
= 36+7
= 43
*Sequence=urutan
So the 9th term of the sequence is 43
So the 9th term of the sequence is 43_______________________________
Detail Jawaban:
Mata Pelajaran: Bahasa Inggris
Kelas: VII (JHS)
Materi: Sequence
Kode: 2.1.1
Tanggal: 9-11-2020
//Semoga membantu.
7. In a geometric sequence, the sum of the first three terms is 76/45 and the sum of the next three terms is 608/1215 . Find the common ratio and the first term of the sequence.
Penjelasan dengan langkah-langkah:
[tex]U_1 + U_2 + U_3 = \frac{76}{45}[/tex]
[tex]a+ar+ar^2 = \frac{76}{45}\\[/tex]
[tex]U_4 + U_5 + U_6 = \frac{608}{1215}[/tex]
[tex]ar^3+ar^4+ar^5= \frac{608}{1215}[/tex]
[tex]r^3(a+ar+ar^2)= \frac{608}{1215}[/tex]
[tex]r^3 \cdot \frac{76}{45}= \frac{608}{1215}[/tex]
[tex]r^3 = \frac{608}{1215} \cdot \frac{45}{76}[/tex]
[tex]r^3 = \frac{4\cdot 152}{5\cdot 243} \cdot \frac{5\cdot 9}{4\cdot 19}[/tex]
[tex]r^3 = \frac{152}{243} \cdot \frac{9}{19}[/tex]
[tex]r^3 = \frac{8\cdot 19}{9\cdot 27} \cdot \frac{9}{19}[/tex]
[tex]r^3 = \frac{8}{27} [/tex]
[tex]r = \frac{2}{3}\\\\[/tex]
[tex]a+ar+ar^2 = \frac{76}{45}[/tex]
[tex]a+\frac{2}{3}a+\frac{4}{9}a = \frac{76}{45}[/tex]
[tex]\frac{9}{9}a+\frac{6}{9}a+\frac{4}{9}a = \frac{76}{45}[/tex]
[tex]\frac{19}{9}a = \frac{76}{45}[/tex]
[tex]a= \frac{76}{45}\cdot \frac{9}{19} [/tex]
[tex]a= \frac{4\cdot 19}{9 \cdot 5}\cdot \frac{9}{19} [/tex]
[tex]a= \frac{4}{5}\\[/tex]
so, the ratio is 2/3 and the first term is 4/5
8. 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
9. 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 ....
10. The second term of a geometric series with a positive ratio is 10 and the 6th term is 160 the sum of the first 10 terms of the series is?
[tex] {r}^{4} = \frac{u6}{u2} = \frac{160}{10} = 16 \\ r = \sqrt[4]{16} = 2 \\a = \frac{u2}{r} = \frac{10}{2} = 5 \\ sn = \frac{a( {r}^{n} - 1)}{r - 1} \\ s10 = \frac{5( {2}^{10} - 1)}{2 - 1} \\ s10 = \frac{5(1024 - 1)}{1} \\ s10 = 5(1023) \\ s10 = 5115[/tex]
11. If the nth term of a sequence is Un =n(n2 + 4), then the 20th term of thatsequence is....
Jawaban:
880
Penjelasan dengan langkah-langkah:
Un=n(2n+4)
U20=20(2.20+4)
U20=20(40+4)
U20=20(44)
U20=880
12. in a geometric sequence,T1= -3, the ratio is 4 and the last term is -3072. how many terms are there is this sequence?
Jawaban:
6
Penjelasan dengan langkah-langkah:
first term = -3
ratio (r) = 4
n term = -3072.
number of terms (n) = ....
Un = a .r^n-1
-3072 = -3 .(4)^n-1
1024 = 4^n-1
4⁵ = 4 ^n-1
n-1 = 5
n = 6.
the numbers of terms = 6
13. The first term of a geometric progression is 75 and the third term is 27. Find the possible values for the fourth term
Jawab:
terlampir
Penjelasan dengan langkah-langkah:
14. the nth term of a sequence is given by 2n2 + 1 .write down first four terms of the squence
Un = 2n²+1
U1 = 2.1²+1 = 2+1 = 3
U2 = 2.2²+1 = 2.4+1 = 8+1 = 9
U3 = 2.3²+1 = 2.9+1 = 18+1 = 19
U4 = 2.4²+1 = 2.16+1 = 32+1 = 33
15. The third term of a geometric progression is -108 and the sixth term is 32. Find (a) the common ratio and first term. [6 marks] (b) [2 marks] the sum of the first 20th term.
Jawab:
(a) Common ratio, r = $\frac{32}{-108} = -\frac{1}{3}$
First term, a = -108
(b) Sum of the first 20 terms, S$_{20}$ = $\frac{a\left(1-r^{20}\right)}{1-r}$
= $\frac{-108\left(1-(-\frac{1}{3})^{20}\right)}{1-(-\frac{1}{3})}$
= $\frac{-108\left(1-\frac{1}{3^{20}}\right)}{\frac{4}{3}}$
= $\frac{-432\left(1-\frac{1}{3^{20}}\right)}{4}$
= $-108\left(3^{19}-1\right)$
= $-108\left(3^{19}\right) + 108$
= $-3245056 + 108$
= -3244948
16. the difference between the tenth term and the seventh term of an arithmetic sequence is -60.the twelfth term divided by the sixth term is 2.find the first term and the common difference.
U10-U7= -60
a= first term , d= common difference
a+9d - (a+6d) = -60
a+9d -a -6d =-60
3d= -60
d= -20
U12/U6 = 2
U12=2U6
a+11d=2(a+5d)
a+11d=2a+10d
d=a=-20
17. Find the first two terms of an arithmetic sequence if the sixth term is 21 and the sum of the first seventeen terms is 0
Jawaban:
56 and 49
Penjelasan dengan langkah-langkah:
u6 = a + 5b = 21
s17 = 0
u9 = a + 8b = 0
-3b = 21
b = -7
a = 56
so the first two terms are 56 and 49
18. The first term of an arithmetic sequence is 14. The fourth term is 32. Find the common difference.
Answer:
The n-th term of an arithmetic sequence is given by:
Un = a + (n - 1)b
Where a the first term, b the common difference. If U4 = 32 and a = 14 then
32 = 14 + (4 - 1)b
18 = 3b
b = 6
The common difference is 6
19. The n term formula of the sequence 20, 16, 12, 8, ... is ....
Jawaban:
20 16 12 8 4 0
semuanya hanya kurang kurang 4
Maaf kalau salah
a = 20b = U2 - U1 = 16 - 20 = -4
rumus barisan aritmatika:
Un = a + (n - 1)b
Un = 20 + (n - 1)(-4)
Un = 20 - 4n + 4
Un = 24 - 4n
atau
Un = -4n + 24
semoga membantu
20. consider the sequence 3,6,9,12... A)find the general term of the sequence B)Find the 11th term of the sequence
Jawaban:
3,6,9,12,...
A) +3 / multiplication 3
B) 3,6,9,12,15,18,21,24,27,30,(33) / 3 × 11 = 33
jawabanny ad 2 ya, yg paling sesuai aj.
semoga membantu:)
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