Question

Show that the progression 11, 5, –1, –7, –13, ......... is an A.P. Write down its (i) first term (ii) common difference (iii) 12th term.

Answer 1

Consecutive differences are equal:

$$5 - 11 = -1 - 5 = -7 - (-1) = -13 - (-7) = -6$$

Hence it is an A.P.

Here $$a = 11$$, $$d = -6$$. 

12th term: $$T_{12} = 11 + (12 - 1) \times (-6)$$

$$= 11 - 66$$

$$= -55$$

So first term = 11, common difference = –6, 12th term = –55.