Find the 5th and the 10th term of the quadratic sequence with T(n)= 3n² + 7.​

1. 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

2. 1. Arithmetic sequence with U2 = 15 and U6 = 31. value of the 10th term?​

Jawab:

Penjelasan dengan langkah-langkah:

1. U2 = 15 = a + b

U6 = 31 = a + 5b

------------- -

-16 = -4b

b = 4. 15 = a + 4

a = 15 - 4 = 11

Un = 11 + 4(n - 1) = 11 + 4n - 4 = 4n + 7

U10 = (4x10) + 7 = 40 + 7 = 47

3. 1. Work out the first three terms and the 10th term of the sequence with the nth term is 2n+ 4 * bisa minta penjelasannya soalnya nggak ngerti​

Jawaban:

To find the first term we substitute n = 1 into the nth term.

1st term =  2(1) + 1 = 3

To find the second term we substitute n = 2 into the nth term.

2nd term =  2(2) + 1 = 5

To find the third term we substitute n = 3 into the nth term.

3rd term =  2(3) + 1 = 7

To find the tenth term we substitute n = 10 into the nth term.

10th term =  2(10) + 1 = 21

Below are a few examples of different types of sequences and their nth term formula.

Type of Sequence

Arithmetic

Geometric

Quadratic

Cubic

Example

6, 2, -2, -6, -10, …

1, 2, 4, 8, 16, 32, …

3, 9, 19, 33, 51, …

2, 22, 78, 188, 370, …

  Nth Term

  10 − 4n

  2n -1

  2n2 + 1

  3n3 − n

4. The second term of a three-term geometric progression of real numbers, where the sum of whose term is sixteen times the sum of their reciprocal, is ... . (1) -2 (2) + (3) 2 (4) 4 The answer is... (A) If (1), (2), and (3) are correct. (B) If (1) and (3) are correct. (C) If (2) and (4) are correct. (D) If only (4) is correct. (E) If all of them are correct.

Jawaban:

[tex] \sqrt{16 = 4} [/tex]

Penjelasan:

D) If only (4) is correct.

#fighting !

5. 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

6. the sum of the first n term of a series is given by sn = 2n(n 3) show that the term of the series form an aritmathic progression

Jawaban:

Note:

It's not clear whether it's  [tex]S_n=2n(n-3)[/tex]  or  [tex]S_n=2n(n+3)[/tex].

So, there will be 2 cases.

Barisan Aritmetika (Arithmetic Progression)

Case 1:  [tex]S_n=2n(n-3)[/tex]

Finding the  [tex]a_n[/tex]  formula

[tex]\large\text{$\begin{aligned}S_n&=2n(n-3)\\a_n&=S_n-S_{n-1}\\&=2n(n-3)-2(n-1)(n-1-3)\\&=2n(n-3)-2(n-1)(n-4)\\&=2n(n-3)-2n(n-4)+2n-8\\&=2n(n-3-(n-4))+2n-8\\&=2n(n-3-n+4)+2n-8\\&=2n(-3+4)+2n-8\\&=2n(1)+2n-8\\&=2n+2n-8\\&=4n-8\\\therefore\ a_n&=\bf4n-8\end{aligned}$}[/tex]

Thus, the term of the  [tex]S_n=2n(n-3)[/tex]  form an arithmetic progression of –4, 0, 4, 8, 12, ... .

The difference between each term equals to 4.

Case 2: [tex]S_n=2n(n+3)[/tex]

Finding the  [tex]a_n[/tex]  formula

[tex]\large\text{$\begin{aligned}S_n&=2n(n+3)\\a_n&=S_n-S_{n-1}\\&=2n(n+3)-2(n-1)(n-1+3)\\&=2n(n+3)-2(n-1)(n+2)\\&=2n(n+3)-2n(n+2)+2n+4\\&=2n(n+3-(n+2))+2n+4\\&=2n(n+3-n-2)+2n+4\\&=2n(3-2)+2n+4\\&=2n(1)+2n+4\\&=2n+2n+4\\&=4n+4\\\therefore\ a_n&=\bf4n+4\end{aligned}$}[/tex]

Thus, the term of the  [tex]S_n=2n(n+3)[/tex]  form an arithmetic progression of 8, 12, 16, 20, 24, ... .

The difference between each term equals to 4, which is the same as case 1.

7. Find the 10th term of each sequence. (a) 19, 28, 37, 46, 55, ... (c) 51, 76, 101, 126, 151, ...

Jawaban:

a.)19,28,37,46,55,64.+9

b.)51,76,101,126,151,176.+25

SemogamembantuTerimakasih

8. 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

9. 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

10. 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

11. 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]

12. 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..

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. on the 10th of November we have?....​

Jawaban:

pada 10 November kami punya

Penjelasan:

semoga bermanfaat ybuat jawaban tercerdas dong

15. 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

16. the like term of the following algebraic expressions :[tex] {3 \times }^{2} - 5 \times + { \times }^{2} [/tex]Is....... And.... Please serius Yg baik tolong bantu :') Makasih :') ​

Jawab:

the like term of the following algebraic expressions :

3x²- 5x + x²

Is 3x² and x²

Penjelasan dengan langkah-langkah:

Like terms" are terms whose variables and their exponents such as the ² in x²) are the same.

In other words, terms that are "like" each other.

17. The average weight of 9 kids is 25 kg. If we add the 10th kid, the averagebecomes 24 kg. The weight of the 10th kid is ​

Jawaban:

15 kg

Penjelasan:

Jawaban:

15 kg

Penjelasan:

maaf klo salah

hanya sekedar saran

18. 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

19. 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

20. 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]