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,

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !