The 6th and 13th term of a geometric progression are 24 and 3/16 respectively.Find the sequence.

clearly, d = (3/16 - 24)/7 = -381/112

Now you can find a, since

a+5d = 24

Now you can list the terms if you want.

it is g.p not a.p!!!!!

To find the common ratio of the geometric progression, we can use the formula:

\[a_n = a_1 \cdot r^{(n-1)}\]

Where \(a_n\) is the \(n\)th term, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.

Given that the 6th term is 24, we can substitute the values into the formula:

\[24 = a_1 \cdot r^{(6-1)}\]
\[24 = a_1 \cdot r^5\]

Similarly, for the 13th term, we have:

\[\frac{3}{16} = a_1 \cdot r^{(13-1)}\]
\[\frac{3}{16} = a_1 \cdot r^{12}\]

Now we have a system of equations:

\[24 = a_1 \cdot r^5\]

\[\frac{3}{16} = a_1 \cdot r^{12}\]

To solve this system of equations, we need to eliminate one of the variables. Dividing the two equations, we obtain:

\[\frac{24}{\frac{3}{16}} = \frac{a_1 \cdot r^5}{a_1 \cdot r^{12}}\]
\[8 = r^7\]

Taking the 7th root of both sides, we find:

\[r = \sqrt[7]{8} = 2\]

Substituting this value back into one of the equations, we can solve for \(a_1\). Using the equation:

\[24 = a_1 \cdot r^5\]
\[24 = a_1 \cdot 2^5\]
\[24 = 32a_1\]
\[a_1 = \frac{24}{32} = \frac{3}{4}\]

Now that we have both the common ratio and the first term, we can generate the rest of the sequence.

To find the sequence of a geometric progression, we need to determine the common ratio (r) and the first term (a₁).

Given that the 6th term is 24, we can use the formula for the nth term of a geometric progression:

aₙ = a₁ * r^(n-1)

Substituting n = 6 and a₆ = 24:

24 = a₁ * r^(6-1)
24 = a₁ * r^5

Similarly, for the 13th term being 3/16:

3/16 = a₁ * r^(13-1)
3/16 = a₁ * r^12

Now we have two equations with the same terms (a₁ and r):

1) 24 = a₁ * r^5
2) 3/16 = a₁ * r^12

To solve this system of equations, we can rewrite equation 2) to have the same exponent as equation 1):

3/16 = a₁ * r^(5*2)
3/16 = a₁ * r^10

Now that both equations have the same power of r, we can equate them:

a₁ * r^5 = a₁ * r^10

Since a₁ is common to both sides, we can cancel it out:

r^5 = r^10

To solve for r, we can take the fifth root of both sides:

r^5^(1/5) = r^10^(1/5)
r = r^2

Now we have r = r^2. Since r ≠ 0 (because it's the common ratio), we can divide both sides by r:

1 = r

Therefore, the common ratio (r) is 1.

Now we can substitute this value of r into either of the original equations to solve for a₁. Let's use equation 1):

24 = a₁ * 1^5
24 = a₁

Hence, the first term (a₁) is 24.

Therefore, the sequence of the geometric progression is: 24, 24, 24, 24, 24, 24, ...