In a geometric sequence, each term is a constant multiple of the preceding one. If the first three terms in a geometric sequence are 22, x, and 28, which of the following could be the sixth term in the sequence?
In a geometric sequence, each term is a constant multiple of the preceding one. If the first three terms in a geometric sequence are 22, x, and 28, which of the following could be the sixth term in the sequence?
In a geometric sequence, the ratio between consecutive terms is constant. Let's denote the common ratio by r. Therefore, we have the second term x = 22r and the third term 28 = 22r^2. Solving for r, we get r^2 = 28 / 22, so r = sqrt(14/11). The sixth term is obtained by multiplying the first term by r^5. Thus, the sixth term is 22 * (sqrt(14/11))^5. Calculating this gives approximately 256.
After many attempts to solve the question, I was unable to reach the same conclusion. Please explain in details