Question

Amelia is starting a new exercise routine. On the first day, she will do 8 sit-ups. On the second day, she will do 12 sit-ups. On the third day, she will do 16 sit-ups. On the fourth day, she will do 20 sit-ups. Write an explicit formula for the sequence of the number of sit-ups Amelia will do.

Answer 1

4 + 4d       d =days so for every day she does 4 more

Answer 2

Day Number of Sit ups

1 8

2 12

3 16

4 20

Second Day- First Day =12 -8=4

Third day - Second day=16-12=4

Fourth Day - Third Day =20 -16=4

Since the Difference between two consecutive terms is same, So it is an Arithmetic Progression.

Through the help of Explicit formula,that is nth term of the sequence ,we can find any term of the sequence.Here

`a=8, d=4\\\\A_(n)=a+(n-1)d\\\\A_(n)=8+(n-1)4=8 +4 n-4\\\\A_(n)=4 n +4`

Explicit Formula for this sequence = 4 n +4, n=Number of days,that is natural number 1,2,3,4,5.......