Solve :

Which term of the arithmetic progression 21, 18, 15,… is -81 ?

Let the n^th term of the progression be -81.
First term a = 21 and common difference = 18 – 21 = -3
Since, a_n = a + (n -1)d
∴ -81 = 21 + (n – 1) × (-3)
⇒ -81 = 21 -3n -3(-1)
⇒ -81 = 21 -3n + 3
⇒ -81- 24 = -3n
⇒ -105 = -3n

⇒ n = 35

Hence, -81 is the 35^th term of the progression.