Show that the progression 6, $5\dfrac{1}{2}, 5, 4\dfrac{1}{2}, 4$,……..is an A.P. Write down its

(i) first term

(ii) common difference

(iii) 9th term.

Series :

$\Rightarrow 6, 5\dfrac{1}{2}, 5, 4\dfrac{1}{2}, 4$

⇒ 6, 5.5, 5, 4.5, 4

Since, 5.5 - 6 = -0.5, 5 - 5.5 = -0.5, 4.5 - 5 = -0.5 and 4.0 - 4.5 = -0.5.

Hence, the series is an A.P. with common difference (d) = -0.5

We know that n^th term of an A.P. is given by,

⇒ a_n = a + (n - 1)d, where a is the first term.

⇒ a₉ = 6 + (9 - 1)(-0.5)

= 6 + 8(-0.5)

= 6 - 4

= 2.

Hence, a = 6, d = -0.5 and a₉ = 2.