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.

Since, 5 - 11 = -6, -1 - 5 = -6, -7 - (-1) = -6 and -13 - (-7) = -6.

Hence, the series is an A.P. with common difference = -6.

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.

⇒ a₁₂ = 11 + (12 - 1).(-6)

= 11 + 11(-6)

= 11 - 66

= -55.

Hence, a = 11, d = -6 and a₁₂ = -55.