Ageometric series where the first term is -12, the last term is -972, and each term after the first is triple the previous term

the geometric series is a(n) = -12(3)^(n-1)

Step-by-step explanation:

"Triple" denotes multiplication by 3.  Thus, the common factor here is 3.

The general formula for a geometric series is a(n) = a(1)(r)^(n-1), where a(1) is the first term, r is the common ratio.

Here, we have a(n)= (-12)(3)^(n-1) = -972.

We need to solve this for n, which represents the last term.

The first step towards solving for n is to divide both sides by -12:

3^(n-1) = 81

To solve for n-1, rewrite 81 as 3^4.  Then we have:

3^(n-1) = 3^4, implying that (n-1) = 4 and that n = 5.

Then we know that it is the 5th term that equals -972.

In summary, the geometric series is a(n) = -12(3)^(n-1).

part a: 1.08

part b: 27.59

multiply length by height. multiply the length by the height, and then double the product. work out 10 x 10 results = 100 square inches, then work out 100 x 2 = 200. the answer is 200 square inches.

step-by-step explanation: