QUESTION 2
Easy
Find the \(10^{th}\) and \(n^{th}\) terms of the GP: 5, 25, 125,...
SOLUTION
1
Identify the first term(a) and common ratio(r)
The GP is: 5, 25, 125, ...
Here, \(a = 5,\, r = \frac{25}{5} = 5\)
Here, \(a = 5,\, r = \frac{25}{5} = 5\)
2
Find the \(10^{th}\) term
\(\begin{aligned} T_{10} &= 5(5)^{10 − 1} \\ &= 5(5)^9\\ &= 5^{10} \\ &= 9,765,625\end{aligned}\)
3
Find the \(n^{th}\) term
\(T_n = 5(5)^{n − 1} = 5^n\)
🏆
Final Answer :
\(T_{10} = 9,765,625\)
\(T_n = 5^n\)
Concept Note
To find any term in a GP, substitute the values of \(a,\, r\) and \(n\).