A pendulum swings through an arc length of 1120 cm (Swing #1). With each further swing, the arc length is reduced by 15 %

State the growth factor.

Calculate the length of the arc in swing #5

I think im supposed to use this formula again, but I don't know how to use it. Tn = ar^n-1

They cagily disguise the growth factor r as a percentage. You need to convert 15% reduction to a scale factor: 85% or 0.85

So, Tn = 1120 * .85^(n-1)

To determine the growth factor, we need to find the common ratio (r) in the geometric sequence that represents the reduction in arc length with each swing.

The formula you mentioned, Tn = ar^(n-1), represents the nth term of a geometric sequence, where:
- Tn is the nth term,
- a is the first term,
- r is the common ratio, and
- n is the number of terms.

In this case, the first term (a) is the initial arc length (1120 cm), and the common ratio (r) is the reduction factor (85% or 0.85, since it's reduced by 15%). Therefore, the formula becomes:

Tn = 1120 * 0.85^(n-1)

Now, let's calculate the length of the arc (#5):

T5 = 1120 * 0.85^(5-1)
= 1120 * 0.85^4
= 1120 * 0.52200625
≈ 585.604375 cm

Therefore, the length of the arc in swing #5 is approximately 585.6 cm.