Question

Consider a sequence given by the formula f(n) = 1 / 3 ^ n−1 starting with n = 1. Generate the first 5 terms of the

sequence.

Answer 1

Explanation:

According to the formula we need to start from n = 1. So the first 5 terms of the sequence, will have the following values of n: 1,2,3,4,5

Now, we need to replace the values of n into the formula to get all the terms.

f(1) = 1/3 ^ 1-1 = 1/3^0 = 1.

This is because any number elevated to zero is always the unit, in this case, 1.

f(2) = 1/3 ^2-1 = 1/3 ^1 = 1/3

This, because any number elevated to 1, is always the same initial number.

f(3) = 1/3 ^3-1 = 1/3 ^2 = 1/9.

Because when the exponent is elevating a fraction number, the power goes to both numbers (numerator and denominator)

f(4) = 1/3 ^4-1 = 1/3 ^3 = 1/27.

f(5) = 1/3 ^5-1 = 1/3 ^4 = 1/81.