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,

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation:

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.