A sequence is defined using tule an=3an-1+n with a1=4. Find the value of a4-a3

Answer 1

Hi, Louisa,

I'm having trouble understanding the equation. You've written:

tule an=3an-1+n

As written, it seems that a value, an, is equal to 3 times itself (3an) minus 1 and then add n.

Is the n a subscript denoting the sequence number?

I wonder if this is what you mean:

A_n = 3A_(n-1) + n

where n is the sequence (1,2,3,4, etc).

I'll show you how my interpretation can be solved, but if my equation is not what you meant, please clarify.

Here is the sequence:

a₄ = 13 and a₃ =9, so a₄ - a₃ = 13 - 9 = 4

Bob

Answer 2

Hi Luisa,

Find a₄ - a₃

Because we know that a₁ = 4, we can plug this into the equation to find a₂.Once we find a₂ we can find a₃ and a₄.

a_n = 3a_n-1 + n

a₁ = 4

a₂ = 3a_{2- 1} + 2

a₂= 3a₁+ 2

a₂= 3(4)+ 2

a₂ = 14

a₃= 3a_{3 - 1} + 3

a₃ = 3a₂ + 3

a₃ = 3(14)+ 3

a₃ = 45

a₄=3a_4-1+4

a₄=3a₃+4

a₄=3(45)+4 = 139

a₄ - a₃ = 139 - 45 = 94

Answer 3

a1 = 3(a0) = 1 = 3(1)+1= 4

a2 = 3(4)+2 = 14

a3 = 3(14) +3 = 45

a4 = 3(45) + 4 = 139

a4 - a3 = 139-45 = 94