Given that A₂=45 and A₃=135 are the 2^nd and 3^rd terms in a geometric sequence, find A₆ . A) 3645 B) 3789 C) 3945 D) 4135 E) None of the above.

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The common ratio (r) of a geometric sequence is given by the ratio of any two consecutive terms. In this case, we have:r = A3 / A2 = 135 / 45 = 3To find A6, we can use the formula for the nth term of a geometric sequence:An = A1 * r^(n-1)where A1 is the first term and n is the term number.Since we don't know A1, we can use the fact that A2 = 45 to find it:A2 = A1 * r^(2-1)45 = A1 * rA1 = 45 / rSubstituting this into the formula for An, we get:An = (45 / r) * r^(n-1)An = 45 * r^(n-2)For A6, we have n = 6, so:A6 = 45 * r^(6-2)A6 = 45 * r^4A6 = 45 * 3^4A6 = 45 * 81A6 = 3645Therefore, the correct answer is A) 3645.

Given That A2=45 and A3=135 Are

Given That A₂=45 and A₃=135 Are