For those which are arithmetic progressions, find out the common difference. (i) 3, 6, 12, 24, ...... (ii) 0, - 4, -8, -12, ......

Question

Find out which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.

(i) 3, 6, 12, 24, ......

(ii) 0, - 4, -8, -12, ......

(iii) \(\frac{1}{2}\),  \(\frac{1}{4}\),  \(\frac{1}{6}\),  \(\frac{1}{8}\), ......

(iv) 12, 2, -8, -18, ......

Answer 1

(i) 3, 6, 12, 24, ......

Common difference,

d₁ = 6 – 3 = 3

Common difference,

d₂= 12 – 6 = 6

Since,

d₁ ≠ d₂

Therefore, it’s not an A.P.

(ii) 0, - 4, -8, -12, ......

Common difference,

d₁ = - 4 – 0 = - 4

Common difference,

d₂= - 8 – (- 4) = - 4 

Since,

d₁ = d₂

Therefore, it’s an A.P. with common difference, d = - 4

(iii)  \(\frac{1}{2}\),  \(\frac{1}{4}\),  \(\frac{1}{6}\),  \(\frac{1}{8}\), ......

Common difference,

Common difference,

Since,

d₁ ≠ d₂

Therefore, it’s not an A.P.

(iv) 12, 2, -8, -18, ......

Common difference,

d₁= 2 – 12 = -10

Common difference,

d₂= - 8 - 2 = -10

Since,

d₁ = d₂

Therefore, it’s an A.P. with common difference, d = - 10