consider the sequence 3,6,9,12... A)find the general term of the sequence B)Find the 11th term of the sequence
1. 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:)
2. the first term is 3 and the fourth is 9. find 11th term.
Jawaban:
suku pertama adalah 3 dan suku keempat 9. temukan suku kesebelas.
Un = a + (n-1)b
ket :
Un = suku ke-n
a = suku pertama
b = beda
b = U_{n} - U_{n-1}b=Un−Un−1
n = banyaknya suku
Unnya 8
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. Enid uses a term to term rule to work out a sequence. The first four terms are 23, 29, 35, and 41. a) Write down the term-to-term rule! b) work out the 11th term of the sequence!
Penjelasan dengan langkah-langkah:
23, 29, 35, 41
a) the number increases by 6
a + (n - 1) d
b)
a + (n - 1) d
a = 23
d = 6
23 + (11 - 1) 6
23 + (10) 6
23 + 60 = 83
11th term = 83
cmiiw if I'm wrong
5. 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:
6. 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
7. 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
8. 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
9. the sum of the first and ninth term of an arithmetic progression is 24.find the sum of the first nine terms of this progression
semoga membantu. maaf, jika salah
10. tolong dong apa arti dari kalimat in1.find the difference between the coefficient of the second term and of the fourth term in the expanded form of the following expression2.find the expanded form of the following algebraic expression
1. Temukan perbedaan antara koefisien istilah kedua dan istilah keempat dalam bentuk ekspres dari ekspresi berikut
2. Temukan bentuk meluas dari ekspresi aljabar berikut
Semoga membantu :) Ans:
1. Temukan perbedaan antara koefisien elemen kedua dan elemen keempat dalam bentuk yang diperluas dari ekspresi berikut.
2. Temukan bentuk yang diperluas dari ekspresi aljabar berikut.
11. 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
12. The fourth term of an AP is 1 and the sum of the first 8 terms is 24. Find the sum of the first 3 terms of the progression. Please help me. Thx.
Let a be the first term and b be the common difference, then
[tex]\begin{array}{rcl}u_4&=&a+3b\\a+3b&+&1\\a&=&1-3b\\\\S_8&=&\frac{8}{2}(2a+7b)\\24&=&4(2(1-3b)+7b)\\6&=&2-6b+7b\\b&=&4\\\\S_3&=&\frac{3}{2}(2a+2b)\\&=&\frac{3}{2}(2(1-3b)+2b)\\&=&\frac{3}{2}(2-6b+2b)\\&=&\frac{3}{2}(2-4b)\\&=&\frac{3}{2}(2-4\times4)\\&=&-21\end{array}[/tex]
13. given the 3rd and 5th term of an arithmetric progression is q + 2p and q+4p respectively find the first term and common difference
Penjelasan dengan langkah-langkah:
a+ 2b = q+2p
a+ 4b = q+ 4p
--------------------- -
-2b = -2p
b = p → a +2(p) = q+2p
a = q
the first term = q
common difference = p
14. Find the length of the diagonal of a rectangle whose sides have lengths 10 dan 18
Penjelasan dengan langkah-langkah:
the length of the diagonal ,= square root of 10 power of 2 adding 18 power of 2
then the value of √ 100+324 = √424
15. If (m+ 1), (2m - 7), and (m + 7) are the 1st,2nd, and 3nd terms of an Arithmetic Sequeace, respectively A. Find m B. Find the formula for finding the nth term. C. Find the 7th term D. Find the sum of the first 10 terms
Jawaban:
C
Penjelasan dengan langkah-langkah:
ngak tau (づ｡◕‿‿◕｡)づ(o´･_･)っ
Jawaban:
C. Find the 7th term
Penjelasan dengan langkah-langkah:
Maaf Kalau salah...
jadikan jawaban terbaik...
jangan lupa follow yaa..
16. 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:
17. 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
18. the first term of an arithmetic progression is 3, the fourth term is 15 and the 16th term is 63, find the common difference of this progression.
Jawab:
b = difference = 4
Penjelasan dengan langkah-langkah:
U1 = 3, U4 = 15, U16 = 63
U1 = a = 3
U4 = a + 3b
15 = 3 + 3b
3b = 15 - 3 = 12
b = 12/3 = 4
19. 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
20. 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
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