Writeanequationtodescribethesequencebelow,andthenfindthe4thterm.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.
5
2
,
3
2
,
9
10
, ...
Write your answer using proper fractions, improper fractions, and integers.
The equation to describe the sequence is:
An = 5 * (4 - n) / (3 - n)
To find the 4th term (n = 4), we plug in n = 4 into the equation:
A4 = 5 * (4 - 4) / (3 - 4)
= 5 * 0 / -1
= 0 / -1
= 0
Therefore, the 4th term is 0.
To write an equation that describes the given sequence, we need to identify the pattern between the terms.
Looking at the sequence: 5, 2, 3/2, 9/10, ...
We can see that each term is obtained by multiplying the previous term by a specific value. Let's call this value "r" for the common ratio.
Therefore, the equation that describes the sequence is:
a(n) = a(1) * r^(n-1)
where a(n) represents the nth term, a(1) is the first term, and r is the common ratio.
To find the 4th term of the sequence, we need to substitute the values into the equation.
Given:
a(1) = 5 (first term)
n = 4 (position of the term we want to find)
Plugging in the values into the equation, we have:
a(4) = 5 * r^(4-1)
a(4) = 5 * r^3
Since we don't know the common ratio (r), it's not possible to calculate the exact value of the 4th term without further information.