Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.

Question

(i) 2, 4, 8, 16, . . .

(ii) 2, 5/2 , 3, 7/2. . .

(iii) – 1.2, – 3.2, – 5.2, – 7.2, . . .

(iv) – 10, – 6, – 2, 2, . . .

(v) 0.2, 0.22, 0.222, 0.2222, . . .

(vi) 0, – 4, – 8, –12, . . .

(vii) 1, 3, 9, 27, . . .

(ix) a, 2a, 3a, 4a, . . .

(xi) a, a², a³, a⁴, . . .

(xiv) 1², 3², 5², 7², . . .

(xv) 1², 5², 7², 7³, . . .

Comments

(ii) 2 , 5/2 , 3 , 7/2

d = 5/2 - 2= 1/2

(iii) -1.2, -3.2 , -5.2

d = -3.2 + 1.2 = -2

(iv) -10 , -6 , -2 , 2

d = -6 + 10 = 4

(vi) 0, -4 , -8 , -12

d = -4 - 0 = -4

(ix) a , 2a , 3a , 4a ..

d = 2a - a = a

So (ii) , (iii) , (iv) , (vi) , (ix) are in Ap