Find the first six terms of the sequence defined by each of these recurrence relations and initial conditions. a) an=6an-1, a0=2
b) an=a2n-1, a1=2
c) an=an-1+3an-2, a0=1 , a1=2
d) an=nan-1+n2 an-2 a0=1 ,a1=1
e) an= an-1+an-3 , a0=1, a1=2 , a2=0

See explanation

Step-by-step explanation:

Solving (a):

where

n = 1

Substitute 2 for

n = 2

Substitute 12 for

n = 3

Substitute 72 for

n = 4

Substitute 432 for

n = 5

Substitute 2592 for

n = 6

Substitute 15552 for

Solving (b):

where

We have

which serves as the first term

n =2

Substitute 2 for

n = 3

n = 4

n =5

n = 6

Solving (c):

 ; ;  

---- First term

n = 2

becomes

Substitute values for a1 and a0

n = 3

becomes

n = 4

becomes

n = 5

becomes

n = 6

becomes

Solving (d):

;     ;

--- First term

n = 2

becomes

n = 3

becomes

n = 4

becomes

n = 5

becomes

n = 6

becomes

Solving (e):

First term:

Second Term:

n = 3

becomes

n = 4

becomes

n = 5

becomes

n = 6

becomes

7 weeks

step-by-step explanation:

convert each fraction to the least common multiple of 20, so 3/4 = 15/20 & 1/10 = 2/20, then divide 15 by 2 and you get a little over 7, so the food will last 7 weeks.

50- 250 is correct i did that one too

step-by-step explanation: