QUESTION 3
Easy
Determine whether 97 and 172 are terms of the sequence \(t_n = 5n − 3\) for \(n ≥ 1\).
SOLUTION
1
Check for 97
Set \(5n − 3 = 97\)
⇒\(5n = 100\)
⇒\(n = 20\)
Since \(n\) is a positive number, 97 is a term of the sequence and it is the \(20^{th}\) term.
⇒\(5n = 100\)
⇒\(n = 20\)
Since \(n\) is a positive number, 97 is a term of the sequence and it is the \(20^{th}\) term.
2
Check for 172
Set \(5n − 3 = 172\)
⇒\(5n = 175\)
⇒\(n = 35\)
Since \(n\) is a positive number, 172 is a term of the sequence and it is the \(35^{th}\) term.
⇒\(5n = 175\)
⇒\(n = 35\)
Since \(n\) is a positive number, 172 is a term of the sequence and it is the \(35^{th}\) term.
Concept Note
Set the general term equal to the given value and solve for \(n\). The value of \(n\) gives the term number.