If x,2x+1 and 3x-2 are GP with 4th term find (a).x (b).common ratio (c).infinity

x / (2x + 1) = (2x + 1) / (3x - 2)

"cross" multiplying ... 3 x^2 - 2 x = 4 x^2 + 4 x + 1 ... x^2 + 6 x + 1 = 0

use quadratic formula to find x

Did you know?

Did you know that in a geometric progression (GP), each term is obtained by multiplying the previous term by a constant value called the common ratio? In this particular case, if the fourth term is 3x - 2, we can determine interesting information about the progression: (a) By comparing the fourth term to the second term (2x + 1), we can set up an equation and solve for x to find the value of x in the progression. (b) Similarly, comparing the second term to the first term (x), we can set up another equation to determine the common ratio between consecutive terms. (c) In a geometric progression, if the common ratio is between -1 and 1, then as the sequence progresses to infinity, the terms approach zero, leading to an infinite geometric series with a sum that can be calculated.