Answer
Distance covered in $15^{th}$ seconds = 464
Total distance covered after 15 seconds = 3600
Work Step by Step
Skydiver falls distance in $1^{st}$ second = 16
Skydiver falls distance in $2^{nd}$ second = 48
Skydiver falls distance in $3^{rd}$ second = 80
Skydiver falls distance in $4^{th}$ second = 112
The distance covered in dives can be expressed in sequence as = 16, 48, 80, 112,.........
From sequence we can see
First term $a^{1}$ = 16
Common distance (d) = 32
Distance covered in $15^{th}$ seconds found by formula of $n^{th}$ term= $a^{1}$ + (n - 1)d
= 16 + (15 - 1)32
= 16 + 448
= 464
Total distance covered after 15 seconds is found by sum formula
$S_{n}$ = $\frac{n}{2}(a_{1} + a_{n})$
$S_{15}$ = $\frac{15}{2}(16 + 464)$ = $\frac{15}{2}\times 480$ = $15\times 240$ = 3600
