Find the eighth term of the geometric sequence whose second and fourth terms are 6 and 54. A)a₈ = 39,366 B)a₈ = 4,374 C)a₈ = 13,122 D)a₈ = 1,458 E)a₈ = 486

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Quizplus · Accepted Answer

To find the eighth term of the geometric sequence, we first need to determine the common ratio. Given the second term (a2 = 6) and the fourth term (a4 = 54), we can use the formula for the nth term of a geometric sequence: a_n = a_1 * r^(n-1). From a2 = a1 * r = 6 and a4 = a1 * r^3 = 54, we can solve for r: r^2 = 54/6 = 9, so r = 3. Now, using a2 = a1 * r = 6, we find a1 = 6/3 = 2. The eighth term is a8 = a1 * r^7 = 2 * 3^7 = 2 * 2187 = 4374.

Find the Eighth Term of the Geometric Sequence Whose Second