if a1 = 4 and an = (an -1) ^2 - 1 then find the value of a4

Answer 1

Hello, Joseph,

Paul M.'s answer is correct. I thought I'd add my comments, in case they help.

I initially had trouble understanding "an = (an -1) ^2 - 1"

I rewrote it: a_n = (a_{n - 1})² - 1

The way it was written, I first thought "an" was a variable from which 1 was subtracted before raising to the 2-1 power.

Using the above interpretation, one finds the same numbers as Paul M.:

Answer 2

Sequence rule:

an = (a_n-1)² - 1

a₁ = 4

Then:

a₁ = 4

a₂ = (4)² - 1 = 16 - 1 = 15

a₃ = (15)² - 1 = 225 - 1 = 224

a₄ = (224)² - 1 = 50176 - 1 = 50175

a₄ = 50175

Answer 3

a1=4

a2=15

a3=224

a4=224² - 1