Final answer:
In a geometric progression, the common ratio is found by dividing any term by the previous term. Using the values given for the 2nd and 4th terms, we can find the common ratio and the first term of the series. By substituting these values into a formula, we can also find the 8th term of the series.
Step-by-step explanation:
In a geometric progression (GP), each term is found by multiplying the previous term by a constant ratio. Let's denote the first term as a, and the common ratio as r. We are given that the 2nd term is 10 and the 4th term is 40. Using these values, we can set up two equations to find the values of a and r. From the 2nd term, we get: a * r = 10. From the 4th term, we get: a * r * r * r = 40. Solving these equations, we find that the common ratio (r) is 2 and the first term (a) is 5. To find the 8th term, we can use the formula: nth term = a * r^(n-1). Plugging in the values, we get: 8th term = 5 * 2^(8-1) = 5 * 2^7 = 640.
Learn more about the concept of geometric progressions