Question

Match each arithmetic sequence with the correct third, fourth, and fifth terms.

Answer 1

1. The first given arithmetic sequence is:

`a_n=-5+(n-1)*3`

To find the third, fourth, and fifth terms, we need to replace n with 3,4, and 5, and solve, so:

`\begin{gathered} a_3=-5+(3-1)*3=-5+2*3=-5+6=1 \\ a_4=-5+(4-1)*3=-5+3*3=-5+9=4 \\ a_5=-5+(5-1)*3=-5+4*3=-5+12=7 \end{gathered}`

The first arithmetic sequence's 3rd,4th, and 5th terms are 1,4,7. Answer a.

2. The second arithmetic sequence is:

`a_n=4+(n-1)*5`

The 3rd,4th and 5th terms are:

`\begin{gathered} a_3=4+(3-1)*5=4+2*5=4+10=14 \\ a_4=4+(4-1)*5=4+3*5=4+15=19 \\ a_5=4+(5-1)*5=4+4*5=4+20=24 \end{gathered}`

The answer is c. 14,19,24

3. The third sequence is:

`a_n=17+(n-1)*13`

The 3rd,4th and 5th terms are:

`\begin{gathered} a_3=17+(3-1)*13=17+2*13=17+26=43 \\ a_4=17+(4-1)*13=17+3*13=17+39=56 \\ a_5=17+(5-1)*13=17+4*13=17+52=69 \end{gathered}`

The answer is b. 43,56,69