Question

A geometric sequence has an initial value of 3 and a common ratio of 2. Which function(s) or formula(s) could represent this situation? Select all that apply. A.f(n) = 3(2)n − 1 B.f(n) = 2(3)n − 1 C.an = 2(an − 1); a1 = 3 D.an = 3(an − 1); a1 = 2

Answer 1

The function an = 2(an-1); a1 = 3 represents the given geometric sequence with an initial value of 3 and a common ratio of 2.

C. an = 2(an-1); a1 = 3

In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio.

In this case, the initial value (a1) is given as 3 and the common ratio is 2.

To represent this situation, we can use the formula an = 2(an-1), where the value of a1 is given as 3. This formula allows us to find any term (an) in the sequence by multiplying the previous term (an-1) by 2.

Using this formula, we can find the subsequent terms in the sequence. For example, a2 = 2(a1) = 2(3) = 6, a3 = 2(a2) = 2(6) = 12, and so on.

The other options, A and B, do not match the given situation. Option A, f(n) = 3(2)n-1, does not represent a geometric sequence because the exponent of 2 should be applied to the previous term, not the common ratio. Option B, f(n) = 2(3)n-1, also does not match the given situation because the initial value of 3 should not be multiplied by 2.