Question

Okay, so I know that simple interest is an arithmetic sequence, T(n) = a + (n-1)d, but cant for the life of me, start at T(0). I am using the example of £100 invested at APR of 5%, and trying to calculate T(0), T(1), T(2) etc.. maybe I can only start at T(1), can anyone answer?

Answer 1

the formula T(n) = a +(n-1)*d implicitly starts at n=1

Answer 2

if you want to start at n = 0, you can just use the formula
T(n) = a + n*d

Answer 3

for simple interest:
Balance = P ( 1 + r*n )
where r = annual interest, n = number of years, P = principal

using T(n) for balance, we have

T(n) = 100 ( 1 + .05*n)
= 100 * 1 + 100*.05*n
= 100 + 5*n

so start at n= 0
T(n) = 100 + 5n

Answer 4

Is the form T(n) = a + n*d the closed form for t(0)?

Answer 5

Yes, I started with a= 100 euro, and then obviously
T1 = a + interest
but my problem was: to be an arithmetic sequence it has to fit the formula:
T(n) = a + (n-1)d
which obviously this doesnt!