A child on a swing is pushed just once. The child moves a distance of 10
feet the first swing, and then only 83%
as much as the previous swing for each one after.

Which of the following sequences expresses the distance the child travels n
swings after the first?
A
an=10(0.83)n
B
an=(10.83)n
C
an=(10.83)n
D
an=10(0.83)n

the distance the child travels n  swings after the first is   . Options A) and D) are identical , so kindly match  with your answer !

Step-by-step explanation:

Here we have , A child on a swing is pushed just once. The child moves a distance of 10  feet the first swing, and then only 83%  as much as the previous swing for each one after. We need to find Which of the following sequences expresses the distance the child travels n  swings after the first . Let's find out:

Initially the distance is 10 feet from after the first swing . It's given that there is 83% as much as previous distance !

For first swing :

⇒

For second swing :

⇒

For third swing :

⇒

⇒

So , For n swings :

⇒

Therefore , the distance the child travels n  swings after the first is   .

Percentages are easy to represent as decimals. Just remember this: If the value is under 100%, just place a decimal point in front of the percent value and remove the percentage sign. If it's over 100%, you'd put the decimal after whatever is in the hundreds place. The reason you can do this is because percent represents a value out of one hundred, and decimals do the same representing values as part of one.
So, 39%->.39