Question

7.1.4 Journal Arithmetic Sequence. Please help me on questions 4 and 5. The picture shows the sequence and what I need to fill out.
Questions:
4. Write the recursive formula for each sequence: an = an – 1 + d.
5. Find the explicit formula for each arithmetic sequence: an = a1 + (n – 1) • d.

Answer 1

Answer:

See below

Step-by-step explanation:

Recursive Formula for Arithmetic Sequences

• $a_n=a_{n-1}+d$
• $a_n$ represents the nth term
• $a_{n-1}$ represents the preceding term
• $d$ represents the common difference

Explicit Formula for Arithmetic Sequences

• $a_n=a_1+(n-1)d$
• $a_n$ represents the nth term
• $a_1$ represents the 1st term
• $d$ represents the common difference

Ernest's Schedule Recursive Formula

We can see that the common difference is $d=0.25$ because for each week, Ernest swims 0.25 more kilometers than the preceding one. Therefore, the recursive formula for Ernest is $a_n=a_{n-1}+0.25$

Ernest's Schedule Explicit Formula

Given our common difference $d=0.25$ from earlier and the fact that $a_1=1$ is our first term, the explicit formula for Ernest is $a_n=1+(n-1)0.25$

Denise's Schedule Recursive Formula

We can see that the common difference is $d=0.5$ because for each week, Denise swims 0.5 more kilometers than the preceding one. Therefore, the recursive formula for Denise is $a_n=a_{n-1}+0.5$

Denise's Schedule Explicit Formula

Given our common difference $d=0.5$ from earlier and the fact that $a_1=1$ is our first term, the explicit formula for Denise is $a_n=1+(n-1)0.5$