Question

Part 1: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for __40____ minutes on Monday. Every day+
she __changed_________ her practice time by ____10 minutes_____. If she continues this pattern, how many minutes will she practice on the 7th day? Be sure to fill in the blanks with the words that will create an arithmetic sequence. Use your scenario to write the function for the 7th term in your sequence using sequence notation.

Answer 1

ah, so an aritmetic sequence can be written in form

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

where $a_n$ is the nth term

$a_1$ is the first term

d is the common difference or how many times it increase or decreases each day

so an example:

Bob swims 2 miles on one day. Every day, he increases his distance by 0.2 miles. If he continues this pattern, how many miles will he swim on the 7th day?

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

$a_7=2+0.2(7-1)$

$a_7=2+0.2(6)$

$a_7=2+1.2$

$a_7=3.2$

bob swims 3.2 miles on the 7th term

also, you can use f(n) instead of $a_n$