QUESTION 1
Easy
Find the \(10^{th}\) and \(26^{th} \) terms of the AP: 3, 8, 13, 18,...
SOLUTION
1
Identify the first term and common difference
In the AP: 3, 8, 13, 18,...
first term, \(a = 3\)
common difference, \(d = 8 − 3 = 5\)
first term, \(a = 3\)
common difference, \(d = 8 − 3 = 5\)
2
Find the \(10^{th}\) term
Using the \(n^{th}\) term formula
\(a_n = a + (n − 1)d\)
\(\begin{aligned} a_{10} &= 3 + (10 − 1) × 5 \\ &= 3 + 45 \\ &= 48\end{aligned}\)
So, \(a_{10} = 48\)
\(a_n = a + (n − 1)d\)
\(\begin{aligned} a_{10} &= 3 + (10 − 1) × 5 \\ &= 3 + 45 \\ &= 48\end{aligned}\)
So, \(a_{10} = 48\)
3
Find the \(26^{th}\) term
\(\begin{aligned} a_{26} &= 3 + (26 − 1) × 5 \\ &= 3 + 125 \\ &= 128\end{aligned}\)
So, \(a_{26} = 128\)
So, \(a_{26} = 128\)
🏆
Final Answer :
\(a_{10} = 48\)
\(a_{26} = 128\)
Concept Note
The \(n^{th}\) term formula is:
\(a_n = a + (n − 1)d\), where
\(a = \) first term
\(d = \) common difference
\(n = \) term number