Answer :
Final answer:
To calculate the common ratio of a geometric progression (GP) with 8 terms, given the first and last terms, you can use the formula for the nth term of a GP. Substituting the known values, you can solve for the common ratio.
Explanation:
A geometric progression (GP) has 8 terms, with the first term being 0.3 and the last term being 38.4. To calculate the common ratio, we can use the formula for the nth term of a GP:
an = a1 * r(n-1)
Given that the first term (a1) is 0.3 and the last term (a8) is 38.4, we can substitute these values into the formula:
38.4 = 0.3 * r(8-1)
Simplifying this equation, we can divide both sides by 0.3:
r7 = 128
Next, we can take the 7th root of both sides to solve for r:
r = 7√128 ≈ 2.256
Therefore, the common ratio of the geometric progression is approximately 2.256.
Learn more about Common ratio of a geometric progression here:
https://brainly.com/question/36023429
#SPJ12
Final answer:
To get the common ratio of a GP, use the formula for the nth term in a GP and substitute the known values. Then, rearrange the formula to isolate 'r'. You can then compute the value of the common ratio.
Explanation:
In a geometric progression (GP) the ratio of any term to its preceding term is constant. This constant is referred to as the common ratio. In this scenario, we have a GP with 8 terms, where the first term (a) is 0.3 and the last term (l) is 38.4/.
To find the common ratio (r), we should use the formula for the nth term in a GP: l = a * r^(n-1). From the details provided, we can substitute a, l and n into the formula: 38.4 = 0.3 * r^(8-1).
If you rearrange to solve for r, you'll get: r = (38.4/0.3)^(1/7). Simplify to get the common ratio.
Learn more about Geometric Progression here:
https://brainly.com/question/4853032
#SPJ12
