Question

The table shows how the number of sits-ups Marla does each day has changed over time. At this rate, how many sits-ups will she do on Day 12? Explain your steps in solving this problem.

Answer 1

61

Explanation

Given that every day Marla does 4 more sit-ups than the previous day, then the number of sit-ups can be modeled by an arithmetic sequence.

Arithmetic sequence formula

`a_n=a_1+(n-1)d`

where

• aₙ: nth term

,

• a₁: first term

,

• d: common difference

The common difference is found by subtracting two consecutive terms as follows:

`d=21-17=4`

Substituting a₁ = 17, n = 12 and d = 4, the number of sit-ups on Day 12 are:

`\begin{gathered} a_(12)=17+(12-1)4 \\ a_(12)=17+11*4 \\ a_(12)=17+44 \\ a_(12)=61 \end{gathered}`