Question

Show that the progression `6, 5 1/2, 5, 4 1/2, 4`, ......... is an A.P. Write down its (i) first term (ii) common difference (iii) 9th term.

Answer 1

Consecutive differences are equal:

$$5\frac{1}{2} - 6 = 5 - 5\frac{1}{2} = 4\frac{1}{2} - 5 = 4 - 4\frac{1}{2} = -\frac{1}{2}$$

Hence it is an A.P.

Here $$a = 6$$, $$d = -\frac{1}{2}$$. 

9th term: $$T_{9} = 6 + (9 - 1) \times(-\frac{1}{2})$$

$$= 6 - 4$$

$$= 2$$

So first term = 6, common difference = `-1/2`, 9th term = 2.