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In a G.P the 3rd term is 4 times the 1st term and the sum of the 2nd term and the 4th term is 30.find the common ratio,find the

STALIN [3.7K]

Answer:

the common ratio is either 2 or -2.

the sum of the first 7 terms is then either 765 or 255

Step-by-step explanation:

a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.

so,

a1

a2 = a1×f

a3 = a2×f = a1×f²

a4 = a3×f = a1×f³

the problem description here tells us

a3 = 4×a1

and from above we know a3 = a1×f².

so, f² = 4

and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).

again, the problem description tells us

a2 + a4 = 30

a1×f + a1×f³ = 30

for f = 2

a1×2 + a1×2³ = 30

2a1 + 8a1 = 30

10a1 = 30

a1 = 3

for f = -2

a1×-2 + a1×(-2)³ = 30

-10a1 = 30

a1 = -3

the sum of the first n terms of a geometric sequence is

sn = a1×(1 - f^(n+1))/(1-f) for f <>1

so, for f = 2

s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765

for f = -2

s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =

= -1×-255 = 255

4 0

2 years ago

The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party,

Mama L [17]

Answer:

$(a)\ P(x = 0) = 0.2725$

$(b)\ P(x \ge 1) =0.7275$

$(c)\ P(x \le 2) = 0.8948$

Step-by-step explanation:

Given

$n = 8$ --- 8 friends

$p = 15\%$ --- proportion that one-time fling

This question is an illustration of binomial probability, and it is represented as:

$P(X = x) = ^nC_x* p^x * (1 - p)^{n-x}$

Solving (a): P(x = 0) --- None has done one time fling

$P(x = 0) = ^8C_0* (15\%)^0 * (1 - 15\%)^{8-0}$

$P(x = 0) = 1* 1 * (1 - 0.15)^{8}$

$P(x = 0) = 0.85^8$

$P(x = 0) = 0.2725$

Solving (b): $P(x \ge 1)$

To do this, we make use of compliment rule:

$P(x = 0) + P(x \ge 1) =1$

Rewrite as:

$P(x \ge 1) =1 - P(x = 0)$

$P(x \ge 1) =1 - 0.2725$

$P(x \ge 1) =0.7275$

Solving (c): $P(x\le 2)$ --- Not more than 2 has one time fling

This is calculated as:

$P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)$

We have:

$P(x = 0) = 0.2725$

$P(x = 1) = ^8C_1* (15\%)^1 * (1 - 15\%)^{8-1}$

$P(x = 1) = 8* (0.15) * (1 - 0.15)^7$

$P(x = 1) = 0.3847$

$P(x = 2) = ^8C_2* (15\%)^2 * (1 - 15\%)^{8-2}$

$P(x = 2) = 28* (0.15)^2 * (1-0.15)^6$

$P(x = 2) = 0.2376$

So:

$P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)$

$P(x \le 2) = 0.2725 + 0.3847 + 0.2376$

$P(x \le 2) = 0.8948$

4 0

2 years ago

PLEASE HELP 50 POINTS 100 students who are in 10th or 11th grade were asked if they participated in at least one extracurricular

Marina86 [1]

There are 2 variables in this problem. One variable is the class number and other variable is the participation in extracurricular activities. Each variable has further two categories. There are two classes: Class 10 and 11. And students either participate or do not participate in extracurricular activities, which makes 2 categories.

The best approach to solve this question is to build a table and start entering the given information in it. When the given data has been entered fill the rest on basis of the data you have.

18 students from grade 11 participate in at least one Extracurricular activities. This means the rest students i.e. 22 students from grade 11 do not participate in Extracurricular activities.

32 students from grade 10 participate in at least one Extracurricular activities. This means total students who participate in at least one Extracurricular activities are 18 + 32 = 50 students.

The rest 50 students do not participate in at least one Extracurricular activities. From these 22 are from class 11. So the rest i.e. 28 are from class 10.

5 0

2 years ago

Judy is selling small candles at the fair for $4 each and large candles for $6 each. She collected $144 selling a total of 28 ca

Pepsi [2]

Answer:

Number of small candles = 12

Number of large candles = 16

Step-by-step explanation:

Total candles = 28

x + y = 28 ---------------(I)

Cost of 'x' small candles = 4 *x = 4x

Cost of 'y' large candles = 6 *y = 6y

Total amount = $144

4x + 6y = 144 -------------(II)

Multiply equation (I) by (-4) and then add the equation. So, x will be eliminated and we can find the value of 'y'

(I) * (-4) -4x - 4y = -112

(II) <u> 4x + 6y = 144</u> {Now, add}

2y = 32

y = 32/2

y = 16

Plug in y = 16 in equation (I)

x + 16 = 28

x = 28 - 16

x = 12

4 0

2 years ago

Read 2 more answers

In an examination, 50%examinees got grade 'A' in mathematics, 75% got grade 'A' in Science, and 35 students got grade 'A' in bot

jasenka [17]

Answer:

15

Step-by-step explanation:

yes it is subtracting by 75-35 then we got the answer who got A in the science only

3 0

2 years ago