QUESTION 3
Easy
Find the \(n^{th}\) term of the AP: 11, 8, 5, 2,... Write the recursive rule for this AP.
SOLUTION
1
Identify the values
In the AP: 11, 8, 5, 2,...
first term, \(a = 11\)
common difference, \(d = 8 − 11 = −3\)
first term, \(a = 11\)
common difference, \(d = 8 − 11 = −3\)
2
Find the \(n^{th}\) term
Using the \(n^{th}\) term formula,
\(a_n = a + (n − 1)d\)
⇒ \(a_n = 11 + (n − 1)(−3)\)
⇒ \(a_n = 11 − 3n + 3\)
⇒ \(a_n = 14 − 3n\)
\(a_n = a + (n − 1)d\)
⇒ \(a_n = 11 + (n − 1)(−3)\)
⇒ \(a_n = 11 − 3n + 3\)
⇒ \(a_n = 14 − 3n\)
3
Write the recursive rule
First term, \(a_1 = 11\)
Each term is obtained by subtracting 3 from the previous term.
\(a_{n+1} = a_n − 3\) for n ≥ 1.
Each term is obtained by subtracting 3 from the previous term.
\(a_{n+1} = a_n − 3\) for n ≥ 1.
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Final Answer :
\(n^{th}\) term, \(a_n = 14 − 3n\)
Recursive rule: \(a_{n+1} = a_n − 3\) for n ≥ 1.
Concept Note
The \(n^{th}\) term formula is:
\(a_n = a + (n − 1)d\), where
\(a = \) first term
\(d = \) common difference
\(n = \) term number
An AP can also be written recursively:
\(a_{n + 1} = a_n + d\)
with the first term specified.