Show that the progression 10, 6, 2, -2, -6,……..is an A.P. Write down its

(i) first term

(ii) common difference

(iii) 10th term.

Since, 6 - 10 = -4, 2 - 6 = -4, -2 - 2 = -4 and -6 - (-2) = -4.

Hence, the series is an A.P. with common difference = -4.

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.

⇒ a₁₀ = 10 + (10 - 1).(-4)

= 10 + (9)-4

= 10 - 36

= -26.

Hence, a = 10, d = -4 and a₂₀ = -26.