Question

Show that the progression 21, 16, 11, 6, 1, ... is an AP. Write its first term and the common difference. Which term of this AP is - 54? .

Answer 1

The given progression is 21, 16, 11, 6, 1, . . .

We have

(16 - 21) = (11 - 16) = (6 -11) = (1 - 6) = -5, which is constant.

So, the given progression is an AP.

Its first term, a = 21 and common difference, d = -5.

Let its nth term be -54. Then,

$T_n=-54\Rightarrow$ a + (n - 1) d = -54

$\Rightarrow$ 21 + (n - 1) $\times$ (-5) = -54

$\Rightarrow$ -5n + 26 = -54 = 5n = 80 $\Rightarrow$ n = 16.

$\therefore T_{16}=-54$

Hence, the 16th term of the given AP is -54.