Respuesta :
Answer: explicit rule: a_n = 11n+31
Recursive rule: a_n = a_n-1 + 11
Step-by-step explanation: explicit rule formula for an arithmic sequence: a_n = a_1 + (n-1)d
d is the common difference which you find by taking one term and subtracting it by the previous term. For example 53-42= 11 or 75-64= 11 so d is 11
a_1 is the first term in the sequence which is 42 in this case.
substitute into formula and get
a_n = 42 +(n-1)(11) then simplify
= 42 + 11n -11
= 11n -31
Therefore a_n = 11n-31
The formula for a recursive rule for an arithmetic sequence is a_n= a_n-1 + d
Substitute and get a_n = a_n-1 + 11
