Answer:
The first term is \(A(1)=5\)
The fourth term is \(A(4)=\frac{11}{2}\).
The tenth term is \(A(10)=\frac{13}{2}\)
Step-by-step explanation:
Given : Arithmetic sequence \(A(n)=5+(n-1)( \frac{1}{6} )\)
To find : The first, fourth, and tenth terms of the arithmetic sequence described by the given rule?
Solution :
Arithmetic sequence \(A(n)=5+(n-1)(\frac{1}{6})\)
Substitute, n=1,4,10 to find the given terms
Put n=1,
\(A(1)=5+(1-1)(\frac{1}{6})\)
\(A(1)=5+(0)(\frac{1}{6})\)
\(A(1)=5\)
The first term is \(A(1)=5\)
Put n=4,
\(A(4)=5+(4-1)(\frac{1}{6})\)
\(A(4)=5+(3)(\frac{1}{6})\)
\(A(4)=5+\frac{1}{2}\)
\(A(4)=\frac{11}{2}\)
The fourth term is \(A(4)=\frac{11}{2}\).
Put n=10,
\(A(10)=5+(10-1)(\frac{1}{6})\)
\(A(10)=5+(9)(\frac{1}{6})\)
\(A(10)=5+\frac{3}{2}\)
\(A(10)=\frac{13}{2}\)
The tenth term is \(A(10)=\frac{13}{2}\)
