Question

Consider the sequence of numbers: b1 =1,b2 =−3, b3 =−7, and =−11. The subscript tells us the value of n. What equation can be used to find the nth term of the sequence?

a) =5−4n
b) =1−4n
c) =−3−4n
d) =−7−4n

Answer 1

The correct equation to find the nth term of the sequence is bn = 5 - 4n. This is revealed by noting the pattern that each term is 4 less than the previous term starting from 1.

Step-by-step explanation:

The sequence of numbers given is b1 = 1, b2 = -3, b3 = -7, and b4 = -11. By examining the sequence, we see that each term is obtained by subtracting 4 from the previous term. Starting from the first term which is 1, we see that the second term (-3) is 1 - 4, the third term (-7) is -3 - 4, and the fourth term (-11) is -7 - 4.

To find a general formula for the nth term of the sequence, we can write an expression that will give us these values when we substitute n = 1, n = 2, n = 3, and so on. Let's represent the nth term of the sequence with bn. Using the pattern that emerges from the terms, we can derive the equation:

bn = 1 - 4(n - 1)

Simplifying this we get, bn = 1 - 4n + 4 or bn = 5 - 4n. Therefore the equation that can be used to find the nth term of this sequence is 5 - 4n.

So, the correct option is a) bn = 5 - 4n.