For an A. P. if t4 = 12, and d = – 10, then find its general term.


4. For an A. P. if t4 = 12, and d = – 10, then find its general term. (3 marks)

Given : For an A.P. t4 = 12, d = – 10

Find : General term (tn)

Sol. tn = a + (n – 1) d
 t4 = a + (4 – 1) d
 12 = a + 3 (– 10)
 a = 12 + 30
 a = 42
tn = a + (n – 1) d
 tn = 42 + (n – 1) (– 10)
 tn = 42 – 10n + 10
 tn = 52 – 10n

 The general term of A.P. is 52 – 10n.