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:
Tn = 2n/(2n + 1)
To find the 4th term, we substitute n = 4 into the equation:
T4 = 2(4)/(2(4) + 1)
T4 = 8/(8 + 1)
T4 = 8/9
Therefore, the 4th term of the sequence is 8/9.
The given sequence seems to be a geometric sequence.
The equation to describe this sequence is:
\(a_n = \frac{5}{2} \cdot \left(\frac{3}{5}\right)^{n-1}\), where \(n\) represents the position of a term in the sequence (starting from 1).
To find the 4th term, substitute \(n = 4\) into the equation:
\(a_4 = \frac{5}{2} \cdot \left(\frac{3}{5}\right)^{4-1}\)
Simplifying this equation:
\(a_4 = \frac{5}{2} \cdot \left(\frac{3}{5}\right)^{3}\)
\(a_4 = \frac{5}{2} \cdot \frac{27}{125}\)
Multiplying the fractions:
\(a_4 = \frac{135}{250}\)
Reducing the fraction to its simplest form:
\(a_4 = \frac{27}{50}\)
Therefore, the 4th term in the given sequence is \(\frac{27}{50}\).