Representing, Naming and Evaluating a Function

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

What is (f+g)(3) for functions f(x)=2x+210 G(x)=2x+125

sashaice [31]

Answer:

347

Step-by-step explanation:

2(3) + 210 = 216

2(3) + 125 = 131

216+131 = 347

3 0

2 years ago

Read 2 more answers

Use the distributive property to rewrite the expression –2(6 – x) without parentheses.

slava [35]

The correct answer is B

8 0

3 years ago

Peter will travel 1,342 kilometers from Paris to Rome. Peter will start his journey at 5:00 A.M. Monday morning and arrive in Ro

Hunter-Best [27]

Answer:

61 km/s

Step-by-step explanation:

First, you count the number of hours he travelled: 22

Next, divide the distance he travelled, 1342, by the time he travelled, 22, $\frac{1342}{22} = 61$

7 0

2 years ago

Drag the tiles to the correct boxes to complete pair. Two cards are drawn from a well-shuffled standard deck of cards. Match eac

joja [24]

Answer:

The correct answers are given below

Step-by-step explanation:

In a deck of 52 cards, there are 4 suits of 13 cards

1) Spade(red)

2). Heart(red)

3). Diamonds (red)

4). Clubs (black)

Each suits area ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3 and 2

To find the probabilities

1). The probability of drawing a red ace followed by another ace of any color without replacement = 2/52 *3/51 = 1/442

2). The probability of drawing a 3 or 5 followed by a 4 or 6 with replacement = 8/52 * 8/52 = 4/169

3). The probability of drawing a king followed by queen with replacement = 4/52 * 4/52 = 1/169

4). The probability of drawing a spade followed by a jack of any color with replacement = 13/52 * 4/52 = 1/52

8 0

3 years ago

Read 2 more answers