All categories

3 years ago

A geometric sequence has a4 = 4 and a5 = 7. What is a1 ? Your answer

Mathematics

1 answer:

svetlana [45]3 years ago

5 0

Answer:

4⁴/7³ or 256/343

Step-by-step explanation:

Given GP with

a₄ = 4
a₅ = 7
a₁ = ?

Let the common difference is r, then

a₅ = a₄r
a₁r³ = 4
a₁r⁴ = 7

Solve for r and then a₁:

4r = 7 ⇒ r = 7/4
a₁(7/4)³ = 4
a₁ = 4*(4/7)³ = 4⁴/7³ = 256/343

You might be interested in

I need an answer asap

Ket [755]

23, because it is a prime number and therefore cannot be simplified enough to take outside of the square root.

3 0

3 years ago

Find the product. (3p – 7)(3p + 7)

hram777 [196]

(3p - 7)(3p + 7) =
(3p × 3p) + (3p × 7) + (-7 × 3p) + (-7 × 7) =
9p^2 + 21p - 21p - 49
= 9p^2 - 49

Therefore, answer would be D.

8 0

3 years ago

Read 2 more answers

The vertices of ΔGHI are G (2, 4), H (4, 8), and I (8, 4). The vertices of ΔJKL are J (1, 1), K (2, 3), and L (4, 1). Which conc

Klio2033 [76]

Answer:

They are similar by the definition of similarity in terms of a dilation.

Step-by-step explanation:

The first step is finding the sides of each triangle.

In triangle GHI, we have that:

GH = sqrt((4-2)^2 + (8-4)^2) = 4.4721

HI = sqrt((8-4)^2 + (4-8)^2) = 5.6569

IG = sqrt((2-8)^2 + (4-4)^2) = 6

Now, for the triangle JKL, we have:

JK = sqrt((2-1)^2 + (3-1)^2) = 2.2361

KL = sqrt((4-2)^2 + (1-3)^2) = 2.8284

LJ = sqrt((1-4)^2 + (1-1)^2) = 3

The triangles are not congruent, because the sides are different

They are similar, because their sides have a proportion (sides of GHI are 2 times the sides of JKL). If they are similar, they have the same angles.

The ratio of their corresponding sides is 1:2, not 1:3

The ratio of their corresponding angles is 1:1, not 1:3

3 0

3 years ago

Alison has some shapes. She has 14 red cubes and 10 red spheres. She has 12 black cubes and 8 black spheres. Alison is going to

KengaRu [80]

Answer:

Step-by-step explanation:

6 0

3 years ago

the length of a rectangle is 4 more than 3 times the width. If the perimeter of the rectangle is 18.4cm, what is the area of the

antoniya [11.8K]

Answer:

A = 10.27cm²

Step-by-step explanation:

Let's represent the width as x,

therefore since the length is 4 more than 3 times the width, it can be represent as 3x + 4, Perimeter = 18.4cm

Perimeter of a rectangle = 2(L + B)

$18.4= 2(3x+4+x)\\18.4= 6x+8+2x\\18.4-8=6x+2x\\10.4=8x\\x=\frac{10.4}{8}\\x=1.3$

width = 1.3cm

Length = 3x + 4 = 3*1.3 + 4 = 7.9cm

Area of a rectangle = length x width

A = 7.9 * 1.3 = 10.27cm²

6 0

2 years ago

Read 2 more answers

A geometric sequence has a4 = 4 and a5 = 7. What is a1 ? Your answer​

A geometric sequence has a4 = 4 and a5 = 7. What is a1 ? Your answer