## a = 6

ar = a+3d

ar^2 = a+9d

so,

d = (ar-a)/3

ar^2 = a+9a(r-1)/3

r^2 = 1+3r-3

r^2-3r+2 = 0

r = 1 or 2

since the GP terms are different, r=2 and d=2 and the sequences are

6,12,24

6,8,10,12,14,16,18,20,22,24

Steve
answered

10 years ago

10 years ago

ar = a+3d

ar^2 = a+9d

so,

d = (ar-a)/3

ar^2 = a+9a(r-1)/3

r^2 = 1+3r-3

r^2-3r+2 = 0

r = 1 or 2

since the GP terms are different, r=2 and d=2 and the sequences are

6,12,24

6,8,10,12,14,16,18,20,22,24

Anonymous
answered

7 years ago

7 years ago

Step-by-Step Bot
answered

1 year ago

1 year ago

The first term of the AP is 6, the fourth term is a, and the tenth term is 6r^6.

We can find the common difference of the AP using the formula a_n = a + (n-1)d, where a_n is the nth term, a is the first term, n is the position of the term, and d is the common difference.

Using this formula, we have:

6 = 6 + (4-1)d => 6 = 6 + 3d => 3d = 0 => d = 0

Since the common difference of the AP is zero, all the terms of the AP are the same.

Since the first term of the AP is 6 and all the terms are the same, we can conclude that the first term of the GP is equal to 6.

So, a = 6

Now, we can find the common ratio of the GP.

The fourth term of the GP is ar^3 = a = 6.

So, 6r^3 = 6.

Dividing both sides of the equation by 6, we get:

r^3 = 1

Taking the cube root of both sides of the equation, we get:

r = 1

Therefore, the common ratio of the GP is 1.

Explain Bot
answered

1 year ago

1 year ago

Let's proceed step by step:

Step 1: Write out the terms of the AP.

The first, fourth, and tenth terms of the AP are given. Let's label them as a, d, and t respectively.

First term (a) = 6

Fourth term (d) = ?

Tenth term (t) = ?

Step 2: Find the common difference of the AP.

To find the common difference (d), we can use the formula:

d = (t - a) / (10 - 1)

Substituting the known values:

d = (t - 6) / 9

Step 3: Find the fourth term of the AP.

We can find the fourth term (d) using the formula:

d = a + 3d

Substituting the known values:

6 + 3d = d

2d = 6

d = 3

Step 4: Find the tenth term of the AP.

Using the formula from Step 2, we can solve for the tenth term (t):

3 = (t - 6) / 9

27 = t - 6

t = 33

Step 5: Find the common ratio of the GP.

Since the first term of the GP is 6 and the fourth term is 3, we can use the formula:

common ratio = fourth term / first term

common ratio = 3 / 6

common ratio = 1/2

Therefore, the common ratio in this geometric progression (GP) is 1/2.