Question

What is the explicit equation for the nth term of the arithmetic sequence 7.2, 3.8, 0.4, -3, -6.4, …?A. an = 7.2 -3.4nB. an = 7.2 + 3.4nC. an = 7.2 - 3.4(n - 1)D. an = 7.2 + 3.4(n + 1)

Answer 1

You can notice that each element of the sequence is lower than the previous one by 3.4. Furthermore, it is necessary that a1 = 7.2 for n=1.

You can notice that the expression which can be express the previous conditions is:

an = 7.2 - 3.4(n - 1)

In fact, if you replace the values for n=1,2,3...

a1 = 7.2

a2 = 7.2 - 3.4(2 - 1) = 7.2 - 3.4 = 3.8

a3 = 7.2 - 3.4(3 - 1) = 7.2 - 6.8 = 0.4

Hence, the arithmetic sequence is 7.2 - 3.4(n - 1)