Question

Question 2 The first five terms of a sequence are shown below. 7,4, 1, -2, -5,... Betsy wants to write a function to represent the sequence in order to find the 75th term of the sequence. Fill in the blanks below with appropriate integer values to complete the function representing the sequence and represent the 75th term of the sequence

Answer 1

In this case we are dealing with an arithmetic sequence, we can represent this kind of sequences with the formula:

f(n) = f0 + d*n

Where f0 is the first term of the sequence and d is the difference between one term and the term that is previous to it.

In this case, f0 equals 7, since this is the value of the first term.

We can find d by taking two terms, let's take for example 1 and 4, by subtracting 4 from 1 we get:

d = 1 - 4 = -3

Then d equals -3 and the formula of the sequence is:

f(n) = 7 + (-3)n

f(n) = 7 - 3n

We can calculate the 75th term by replacing 75 for n, then we get:

f(75) = 7 - 3 * 75 = -218

Then f(75) equals -218