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A sequence is given by \(2\frac{1}{2}, 5, 7\frac{1}{2}, .....\) if the nth term ...


Question

A sequence is given by \(2\frac{1}{2}, 5, 7\frac{1}{2}, .....\) if the nth term is 25, find n

Options

A) 9

B) 10

C) 12

D) 15

The correct answer is B.

Explanation:

\(a = 2\frac{1}{2}, nth = a + (n-1)d \Rightarrow 25 = 2\frac{1}{2} + (n-1)2\frac{1}{2}\\25 = \frac{5}{2}+(n-1)\frac{5}{2} \Rightarrow 22\frac{1}{2} = \frac{5n-5}{2}\Rightarrow \frac{45}{2} = \frac{5n-5}{2}\\45 = 5n - 5 \Rightarrow 5n = 50 \Rightarrow n = 10\)

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Dicussion (1)

  • \(a = 2\frac{1}{2}, nth = a + (n-1)d \Rightarrow 25 = 2\frac{1}{2} + (n-1)2\frac{1}{2}\\25 = \frac{5}{2}+(n-1)\frac{5}{2} \Rightarrow 22\frac{1}{2} = \frac{5n-5}{2}\Rightarrow \frac{45}{2} = \frac{5n-5}{2}\\45 = 5n - 5 \Rightarrow 5n = 50 \Rightarrow n = 10\)

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