Find the twenty fifth term of the A. P. : 12, 16, 20, 24, ..... (2 marks)

1. Find the twenty fifth term of the A. P. : 12, 16, 20, 24, ..... (2 marks)

Sol. For the given A.P. 12, 16, 20, 24, .....

Here, a = t1 = 12

d = t2 – t1 = 16 – 12 = 4

We know,

tn = a + (n – 1) d

 t25 = a + (25 – 1) d

 t25 = 12 + 24 (4)

 t25 = 12 + 96

 t25 = 108

 The twenty fifth term of A.P. is 108.

(v) 2, 6, 12, 20, 30, ... (1 mark)

(v) 2, 6, 12, 20, 30, ... (1 mark)

Sol. t₁ = 0 + 2 = 2

t₂ = 2 + 4 = 6

t₃ = 6 + 6 = 12

t₄ = 12 + 8 = 20

t₅ = 20 + 10 = 30

t₆ = 30 + 12 = 42

t₇ = 42 + 14 = 56

t₈ = 56 + 16 = 72

t₉ = 72 + 18 = 90

∴  The next four terms of the sequence are 42, 56, 72 and 90.