Question

1. in a geometric series, where \\(r = 3\\) and \\(s_6 = 5465\\), determine the first term in the sequence.

1. a ball is dropped from a height of 15 metres above ground. after the ball touches the ground it bounces to 60% of its previous height. determine how far the ball has traveled vertically when it hits the ground for the \\(4^{\text{th}}\\) time. round your answer to the nearest tenth of a metre.

Explanation:

Question 7: Identify given values and formula for geometric series sum

$$
LATEXBLOCK0
$$

Question 7: Solve for the first term \(a\)

$$
LATEXBLOCK1
$$

Question 8: Calculate total vertical distance for 4 ground hits

$$
LATEXBLOCK2
$$

Answer:

Question 7

The first term in the sequence is \(5\).

Question 8

The total vertical distance the ball has traveled when it hits the ground for the \(4^{\text{th}}\) time is \(50.3\text{ m}\).