Question

which of the following are APs? if they form an AP, find an AP, find the common difference d and write three more terms: (i) 2,4,8,16... (ii) -1.2,-3.2,-5.2,-7.2,. (iii) 3,3+√2,3+2√2,3+3√2... (iv) 0,-4,-8,-12​

Answer 1

Answer:

i) a2-a1= 4-2=2 ----1)

a3-a2= 8-4=4 ----2)

Since, 1) ≠ 2)

It is not an A.P.

ii) a2-a1= -3.2-(-1.2)= -2.0 ----1)

a3-a2= -5.2-(-3.2)= -2.0 ----2)

Since, 1)= 2)

It is an A.P.

Common difference = 2.0

Next terms are, -9.2,-11.2, -13.2....

iii) a2-a1= √2 ----1)

a3-a2= √2 ----2)

Since, 1) =2)

It is an A.P.

Common difference = √2

Next terms are, 3+4√2, 3+5√2, 3+6√2....

iv) a2-a1= -4 ----1)

a3-a2= -4 ----2)

Since, 1) = 2)

It is an A.P.

Common difference = -4

Next terms are, -16, -20, -24....

Hope it helps