A geometric progression is given: 2, 6, 18 … Find the number of the sequence term equal to 162.

To solve this problem, remember, a geometric progression is a sequence in which each subsequent number, starting from the second, is obtained from multiplying the previous one by a certain number q.
Any member of a geometric progression can be calculated by the formula: bn = b1 * q ^ n-1. b1 = 2. Calculate the difference: q = 6/2 = 3, bn = 162. Substitute the values into the formula.
162 = 2 * 3 ^ n-1,
162/2 = 3 ^ n-1,
81 = 3 ^ n-1;
3 ^ 4 = 3 ^ n-1;
4 = n-1;
n = 4 + 1;
n = 5.
The 5th term of this geometric progression is 162.