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tamaranim1 [39]
3 years ago
10

The sum of the first three terms of geometric sequence is 14. If the first term is 2, find the possible values of the sum of the

first 5 terms.
Mathematics
2 answers:
Scorpion4ik [409]3 years ago
7 0

We have a first term of 2 and a common ratio of <em>r</em>. We're told

2 + 2r + 2r^2 = 14

r^2 +r  - 6 = 0

(r+3)(r-2)=0

r=-3 \textrm{ or } r=2

If r=-3 the fourth term is 2((-3)³) and the fifth 2((-3)^4) for a sum of

14 - 54 + 162 = 122

If r=2 the remaining terms are 2(2^3)=16 and 2(2^4)=32 for a sum of

14 + 16 + 32 = 62

Answer: 62 or 122

Irina18 [472]3 years ago
4 0

Geometric series are in the form of

a +a*r +a*r^2+...

Where a is the first term and r is the common ratio .

And it is given that

2 +2*r +2*r^2=14

2r^2+2r-12=0

r^2 +r-6=0

(r+3)(r-2)=0

r=-3,2

So the first five terms are

2+2(-3)+2(-3)^2+2(-3)^3+2(-3)^4  or 2+2(2)+2(2)^2+2(2)^3+2(2)^4

= 2-6+18-54+162 or 2+4+8+16+32

= 122 or 62

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A marketing firm tracks data on grocery store visits. In one study, it finds that the probability that a shopper buys bread duri
timurjin [86]

Answer:

Option B.

Step-by-step explanation:

Two events are said to be independent of each other, if the probability of one event ocurrin in not way affects the probability of the other event occurring.

The interception of two independent events P(A ∩ B) = P(A) × P(B), where:

P(A) = 0.70

P(B) = 0.20

P(A ∩ B) = P(A) × P(B) = 0.70x0.20 = 0.14

The two events are independent if the probability of buying Bread AND cheese equals: 0.14, which is Option B.

7 0
3 years ago
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The sprit club is making school jackets to sell. The cost c (in dollars) for silkscreening supplies and jackets is c=20x+270, wh
lys-0071 [83]

Answer:

The club must sell 18 jackets to break even

Step-by-step explanation:

Given:

C = 20x + 270

Where,

x = number of jackets

Equation for revenue R in terms of the number of jackets

Revenue = price × quantity

Price of the jacket = $35

Quantity of the jacket = x

Revenue = price × quantity

= 35 * x

R = 35x

Break even point is the point at which cost is equal to revenue, that is, no gain; no loss.

Cost = revenue

20x + 270 = 35x

270 = 35x - 20x

270 = 15x

x = 270 / 15

= 18

x = 18 jackets

The club must sell 18 jackets to break even

3 0
3 years ago
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I need all the spaces filled in please :)
Artist 52 [7]

Answer:

3x + y = -16      

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given a system of equations are

        5x+6y =-5  

       - 2x  - 5y = -11

multiply '1' and Adding two system of equtions

                 + 1      (5x   +  6y   =  -5)

                + 1      (<u> -2x    -   5y  =   -11)</u>

                   <u>       3x    +    y   = -16           </u>

<u>Final answer:-</u>

                          5x   +  6y   =  -5

                        <u> -2x    -   5y  =   -11</u>

                   <u>       3x    +    y   = -16           </u>

<u />

7 0
3 years ago
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Llana [10]

The set \{x\mid x^4-x^3-x^2-6x+6=0\} is the set of all values of x that are solutions to the given equation. So all you need to do is check whether x=1 and x=2 satisfy the equation.

x=1\implies 1^4-1^3-1^2-5+6=0

x=2\implies2^4-2^3-2^2-10+6=0

The equation holds, so both 1 and 2 are solutions, and hence \{1,2\} is a subset of the solutions.

6 0
3 years ago
What does multiplication translate to when using logs?
4vir4ik [10]
It translates to addition.
6 0
3 years ago
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