Question

Renee belongs to a bowling club. She scores 50, 52, 55, and 59 on her first four games. She hopes to continue improving according to this pattern. Part A: What are the next four terms in Renee’s sequence?
Part B: Write an recursive function rule for the sequence?
Part C: What is the domain and range of your function rule?
Part D: Do you think Renee can keep up this pattern? Explain.

Answer 1

terms differ by 2,3,4,...
2+3+4+...+n = n(n+1)/2-1
so, the sequence is

Tn = 49 + n(n+1)/2
50,52,55,59,64,70,77,85,...

T1 = 50
Tn = T(n-1) + n

T21 = 280
T22 = 302

So, she can't keep it up past 21 games.

Answer 2

Thank you