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.