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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:

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

## Dicussion (1)

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