Question

On October 1st Nadia starts a push-up challenge by doing 18 push-ups. On October 2nd, she does 21 push ups on October 3rd, she does 24 push-ups. She continues until October 16th. How many push ups does she do on October 16th.

Answer 1

63 pushups

Step-by-step explanation:

On October 1, the number of pushups = 18

On October 2, the number of pushups = 21

On October 3, the number of pushups = 24

We have the number pattern: 18, 21, 24, ...

We observe that:

18+3 = 21; and

21+3 = 24

Therefore, this is an arithmetic sequence where:

• The first term, a = 18

,

• The common difference, d= 3

October 16 will be the 16th day since she started, therefore: n=16

We are to determine the 16th term of the sequence.

For an A.P.

`\text{nth term, }U_n=a+(n-1)d`

Therefore, the 16 term will be:

`\begin{gathered} U_(16)=18+(16-1)3 \\ =18+15(3) \\ =18+45 \\ =63 \end{gathered}`

Nadia will do 63 pushups on October 16th.