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.

(ix) 2, 4, 8, 16, ..... (1 mark)

(ix) 2, 4, 8, 16, ..... (1 mark)

Sol. t₁ = 2¹ = 2

t₂ = 2² = 4

t₃ = 2³ = 8

t₄ = 2⁴ = 16

t₅ = 2⁵ = 32

t₆ = 2⁶ = 64

t₇ = 2⁷ = 128

t₈ = 2⁸ = 256

∴  The next four terms of the sequence are 32, 64, 128 and 256.

Find the next two terms of the given sequence 2, 4, 8, 16, ...........