Which choice is the explicit formula for the following geometric sequence?0.3, –0.06, 0.012, –0.0024, 0.00048, ...A.an = –0.3(0.2)(n – 1)B.an = 0.3(0.2)nC.an = –0.3(–0.2)(n – 1)D.an = –0.2(0.3)(n – 1)E.an = 0.3(–0.2)(n – 1)SUBMITarrow_backPREVIOUS
Question
Which choice is the explicit formula for the following geometric sequence?0.3, –0.06, 0.012, –0.0024, 0.00048, ...A.an = –0.3(0.2)(n – 1)B.an = 0.3(0.2)nC.an = –0.3(–0.2)(n – 1)D.an = –0.2(0.3)(n – 1)E.an = 0.3(–0.2)(n – 1)SUBMITarrow_backPREVIOUS
Solution
The explicit formula for a geometric sequence is given by an = a1 * r^(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.
In this sequence, the first term a1 is 0.3.
The common ratio r can be found by dividing any term by the previous term. For example, -0.06 / 0.3 = -0.2.
So, the explicit formula for this sequence is an = 0.3 * (-0.2)^(n-1).
Therefore, the correct answer is C. an = –0.3(–0.2)(n – 1).
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