A sequence is given by \(2\frac{1}{2}, 5, 7\frac{1}{2}, .....\) if the nth term is 25, find n
A
9
B
10
C
12
D
15
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(a = 2\frac{1}{2}, nth = a + (n-1)d \Rightarrow 25 = 2\frac{1}{2} + (n-1)2\frac{1}{2}\\
25 = \frac{5}{2}+(n-1)\frac{5}{2} \Rightarrow 22\frac{1}{2} = \frac{5n-5}{2}\Rightarrow \frac{45}{2} = \frac{5n-5}{2}\\
45 = 5n - 5 \Rightarrow 5n = 50 \Rightarrow n = 10\)
Source: Myschool Past Questions Archive (Record #26693)