(3) Which term of the arithmetic sequence is 24, 23 ¼ ,22 ½, 21 ¾, ………. Is 3?

Solution :

First term = 24

a = 24

Common difference = t2 – t1

 = 23 ¼ – 24

 = (93/4) – 24

 = (93-96)/4

d  = -3/4

tn =  a + (n - 1) d

Let us consider 3 as nth term

tn  = 3

3  = 24 + (n-1) (-3/4)

3 – 24  = (n-1)  (-3/4)

(-21 x 4)/(-3)  = n -1

84/3  = n -1

28  = n – 1

28 + 1  = n

  n =  29

Hence, 29th term of and A.P is 3.