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.
1. 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]
2. 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:)
3. 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.
4. Hence, find the 200th term sequence 10,14,18,22,26
Penjelasan dengan langkah-langkah:
10, 14, 18, 22, 26, ...
Un = a + (n - 1)b
a = 10
b = 14 - 10 = 4
U200 = 10 + (200 - 1) 4
U200 = 10 + (199)4
U200 = 10 + 796
U200 = 806
The 200th term sequence 10,14,18,22,26,... is 806.
5. 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
☺
6. 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
7. (Total fo Question 10 Here are the first four terms of a number sequence: 25.22. 19. 16.. (a) Find the next two terms of the sequence. (b) Find a formula for the nth term of the sequence. 1
[tex]a).d = a2 - a1 = 22 - 25 = - 3 \\ 16 - 3 = 13 \\ 13 - 3 = 10 \\ the \: next \: two \: terms \: are \: 13 \: and \: 10 \\ \\ b).the \: {n}^{th} \: formula \\ un = a1 + (n - 1)d \\ un = 25 + (n - 1) - 3 \\ un = 25 - 3n + 3 \\ un = - 3n + 28[/tex]
8. Find the 5th and the 10th term of the quadratic sequence with T(n)= 3n² + 7.
T(n) = 3n² + 7
T(5) = 3.5² + 7
= 3.25 + 7
= 75 + 7
= 82
T(10) = 3.10² + 7
= 3 . 100 + 7
= 300 + 7
= 307
9. 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???
10. 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
11. 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
12. bantu plsKnown the geometric sequence is 9, 27, 81, . . . Find the 10th term!Diketahui barisan geometri tersebut adalah 9, 27, 81, . . .Tentukan suku ke-10!
Jawaban:
177,147
Penjelasan dengan langkah-langkah:
9 adalah hasil dari 3²
27 adalah hasil dari 3³
3²,3³,3⁴,3⁵,3⁶,3⁷,3⁸,3⁹,3¹⁰,3¹¹
suku ke10 adalah 3¹¹ yaitu 177,147
13. consider this sequence 3,6,12,24,48,find in the term of. ,the formula of the nth term of this sequence
Jawaban:
the formula was 3.2^n
while n is respective number from 0 to unlimited. but its a round number, not partial one
14. 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
15. Consider the sequence 10, 14, 18, 22, 26, ... (i) Write down the next two terms of the sequence. (ii) Find, in terms of n, a formula for the nth term of the sequence. (iii) Hence, find the 200th term.
10, 14, 18, 22, 26
(i)
b = 4
Next two terms = 30, 34
(ii)
Un = bn + (U1 - b)
Un = 4n + (10 - 4)
Un = 4n + 6
(iii)
U200 = 4(200) + 6
U200 = 800 + 6
U200 = 806
Maaf kalau rumus nya dalam B.Indo soalnya gatau dalam B.Inggris kayak gimana, tapi soalnya aku ngerti kok.
16. Consider the sequence 9, 16, 25, 36, 49, ...(1) Write down the next two terms of the sequence.(1) Find, in terms of n, a formula for the termof the sequence.(iii) Hence, find the 25 term.
Penjelasan dengan langkah-langkah:
(i) 64, 81
(ii) [tex]U_n = (n+2)^2 [/tex]
(iii) [tex] U_{25} = (25+2)^2 = 27^2 = 729 [/tex]
Jawab:
1. 64, 81
2. n^2, (n + 1)^2, (n + 2)^2, (n + 3)^2
3. 784
Penjelasan dengan langkah-langkah:
17. find the nth term of the sequence 3,8,15,24
Polanya itu ditambah terus sama bilangan ganjil
3(+5), 8(+7), 15(+9), 24
Jadi bilangan selanjutnya 24 + 11 = 35
18. 1. Consider the sequence 4,11,18,25,32, .a) Find, in terms of n, a formula for the nthterm of the sequenceb) Hence, find the 93rd termc) The nth term of the sequence is 158, find the value of n
Jawaban:
a) 7n - 3
b) the 93rd term = 648
c) the value of n = 23, (or the 23rd term)
Penjelasan dengan langkah-langkah:
the way to find answers are attached
19. look at the following sequence 2 , 9 , 16 , 23 , 30 a. find the next two terms of the sequence final answer: b. find the general term of the sequence final answer: Tn = c. is 78 a term of the sequence? final answer (answer with yes or no) d. in which term/position will 632 appear in the sequence? final answer: ......... term
Jawaban:
a. 37, 44
b. Tn= 9+7n
c. no
d. 91
Penjelasan:
a. b= U2-U1= 9-2 = 7
maka angka selanjutnya adalah 30+7=37 dan 30+7.2=44
b. Tn=Un= a+b(n-1)
a= 2; b=7
maka Tn = 2+7(n-1) = 9+7n
c. (78-2)/7 akan menghasilkan sisa sehingga tidak termasuk
d. n= 1+[(632-2)/7] = 1+90 = 91
20. 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:
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