Question

Given the sequences -2a * n - 1 and a * 2 = 12, write the explicit formula for a * n.

A) a * n = 6 * 2^(n-1)
B) a * n = 12 * 2^(n-1)
C) a * n = 6 * 2^n
D) a * n = 12 * 2^n

Answer 1

The explicit formula for a * n is a * n = -12n - 1.

Step-by-step explanation:

To find the explicit formula for a * n, we need to solve the given equation a * 2 = 12 for 'a'. Dividing both sides of the equation by 2 gives us a = 6. Substituting this value of 'a' into the expression -2a * n - 1, we get -2 * 6 * n - 1, which simplifies to -12n - 1.

Therefore, the explicit formula for a * n is a * n = -12n - 1.

So, the correct answer is D) a * n = 12 * 2^n.