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8_murik_8 [283]

2 years ago

13

Classify the sequence {a_n}={4,10/3,8/3,2...} as arithmetic or geometric. Then, determine whether the sequence is convergent or

divergent.

2 answers:

muminat2 years ago

8 0

Answer:

Arithmetic and divergent sequence.

Step-by-step explanation:

Tresset [83]2 years ago

4 0

Answer:

Arithmetic and divergent sequence.

Step-by-step explanation:

We have been given a sequence:

$a_n=4,\frac{10}{3},\frac{8}{3},2...$

Arithmetic sequence: It is the sequence in which the difference (known as common difference) between consecutive terms is same

Formula for difference: $d=a_n-a_{n-1}$

Geometric sequence: It is the sequence in which the ratio (known as common ration) between consecutive terms is same.

Formula for ratio: $\frac{a_n}{a_{n-1}}$

Here, we will first check the common difference

$d=\frac{10}{3}-4=\frac{-2}{3}$

$\frac{8}{3}-\frac{10}{3}=\frac{-2}{3}$

$2-\frac{8}{3}=\frac{-2}{3}$

Hence, we are getting common difference therefore it is an arithmetic sequence.

Arithmetic sequence always diverges

And given sequence being arithmetic will diverge.

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Consider the equation 4x2 + 2x = (x + 2)(x − 5)x Match the Property used to create an equation with the same solution set. optio

mel-nik [20]

Factor then solve. Exact Form: x = 0 , 7 + √ 97 2 , 7 − √ 97 2 Decimal Form: x = 0 , 8.42442890 … , − 1.42442890 …

8 0

2 years ago

1) Omar has scored 85, 71, and 77 on the first three exams in his math class. If the standard 70,80,90 scale is used for grades

Rus_ich [418]

Answer:

a. 47

b. 87

c. 127

Step-by-step explanation:

Assume a total of 4 exams ( first 3 plus a final)

Let final score be X,

Hence, average score = (85 + 71 + 77 + x) / 4 = (233 + x) / 4

a) to get a C, the average score must be 70

70 = (233 + x) / 4

(233 + x) = 70 (4) = 280

x = 280 - 233 = 47 (Ans)

b) to get a B, the average score must be 80

80 = (233 + x) / 4

(233 + x) = 80 (4) = 320

x = 320 - 233 = 87 (Ans)

c) to get a A, the average score must be 90

90 = (233 + x) / 4

(233 + x) = 90 (4) = 360

x = 360 - 233 = 127 (Ans)

6 0

2 years ago

Kitty [74]

Answer:

2

Step-by-step explanation:

6 0

2 years ago

3x2 + 2(x2 – 20) = 16 - 2x2

lana66690 [7]

3x(2) + 2(2x - 20) = 16 - 2x(2)

6x + 4x - 40 = 16 - 4x

10x - 40 = 16 - 4x

14x - 40 = 16

14x = 56

x = 4

Hope this helps! ;)

8 0

2 years ago

Help me asap! I will give you marks

Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

6 0

8 months ago