Write a rule to find the nth term for an arithmetic sequence given the following:

a3 = 14
a12 = 59

recursive rule: ?
explicit rule: ?

write an explicit and recursive rule for a sequence given the following:

a4 = 2
r = 1/3

recursive rule: ?
explicit rule: ?

ANSWER

See explanation

EXPLANATION

Question 1:

The third term of the arithmetic sequence is :

14=a+2d...(1)

The twelveth term is

59=a+11d...(2)

Subtract equation (1) from (2)

45=9d

This implies that

d=5

a=14-2(5)=4

The explicit rule is;

Recursive formula:

Question 2

The geometric sequence has the fourth term to be 2 and the common ratio to be r=⅓

This implies that,

This implies that,

The explicit rule:

The recursive rule is

where,

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.

idk

step-by-step explanation: