Question

A sequence can be generated by using an=a(n-1)+4. If a1=2, what is the value of a20?

Answer 1

In a sequence of numbers, a2=9, a3=7, and a4=5. Based on this information, which equation can be used to find the nth term in the sequence an?




In a sequence of numbers, a2=9, a3=7, and a4=5. Based on this information, which equation can be used to find the nth term in the sequence an?


an=9-2n


an=13n-2


an=9n-2


an=13-2n

Answer 2

To find the value of a20 using the given sequence formula an=a(n-1)+4 and initial value a1=2, we can plug in the values and calculate:

a2 = a1 + 4 = 2 + 4 = 6
a3 = a2 + 4 = 6 + 4 = 10
a4 = a3 + 4 = 10 + 4 = 14

Continuing in this way, we can see that the sequence follows the pattern a(n) = 4n - 2.

Therefore, to find a20, we plug in n=20:

a20 = 4(20) - 2 = 80 - 2 = 78

Therefore, the value of a20 is 78.

Answer 3

To find the equation that can be used to find the nth term in the sequence an based on the given information, we can first observe the pattern in the given values of a2=9, a3=7, and a4=5.

From a2 to a3, we subtract 2, and from a3 to a4, we also subtract 2. This indicates that there is a common difference of -2 between the terms.

Therefore, the equation that relates the position of the term in the sequence and the value of that term is:

an = 11 - 2n

The correct equation based on the information provided is:

**an = 11 - 2n**