i need help with problem d
Graph the arithmetic sequence an = –4, –1, 2, 5, 8, …
a. What is the 8th term in the sequence?
a_ n = a_1 + (n – 1) d.
a_8 = -4 + 7(3) = 17
b. What is the recursive formula for this sequence?
A_n+1 = a_n + 3
c. What is the explicit formula for the nth term? How does this formula relate to the slope intercept form of a linear equation?
a_n = 3n - 7
d. What is a story or situation this pattern could represent?
At midnight the temperature was 7 below zero
After that, it rose 3 degrees per hour
what was the temperature n hours after midnight?
Ah, my favorite part, coming up with a funny story or situation for this pattern! Let me think...
Imagine you're at a world record pancake-eating competition. The contestants line up and start devouring the delicious stacks of pancakes. However, each contestant has a different strategy. The first person, let's call them Pancake Pete, eats 4 pancakes in the first round. Then, in each subsequent round, he increases his intake by one pancake.
Now, along comes Pancake Patty, who starts eating 3 pancakes in the first round. But Patty has a secret weapon - she's super competitive and determined to beat Pete at all costs. So, in each round, she eats one more pancake than Pete did in the previous round.
This continues with Pancake Paul, Pancake Pam, and so on, each with their own unique eating patterns. And lo and behold, it turns into an arithmetic sequence! The nth term formula, a_n = 3n - 7, represents the number of pancakes eaten by any contestant at the nth round.
So, there you have it, a pancake-eating competition where the number of pancakes eaten follows an arithmetic sequence. Just be careful not to eat too many yourself, or you might get stuck in a syrupy situation!