Question

Which of the following sequences form an AP?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11…….

(iii) -1, -1.25, -1.5, -1.75……

(iv) 1, -1, -3, -5…………

• A. (i) and (iv)
• B. (ii) and (iv)
• C. (iii) and (iv)
• D. (i),(iii) and (iv)

Answer 1

The correct option is C

(iii) and (iv)

Consider each list of numbers:
(i) 2, 4, 8, 16……..

Difference between the first two terms = 4 - 2 = 2

Difference between the third and second term = 8 - 4 = 4

Since $a_2–a_1\ne a_3–a_2$, this sequence is not an AP.

(ii) 2, 3, 5, 7, 11……..

Difference between the first two terms = 3 - 2 = 1

Difference between the third and second term = 5 - 3 = 2

Since $a_2–a_1\ne a_3–a_2$, this sequence is not an AP.

(iii) -1, -1.25, -1.5, -1.75…….

Difference between the first two terms = -1.25 – (-1) = -0.25

Difference between the third and second term = -1.5 – (-1.25) = -0.25

Difference between the fourth and third term = -1.75 – (-1.5) = -0.25

Since $a_2–a_1=a_3-a_2=a_4-a_3$, this sequence is an AP.

(iv) 1, -1, -3, -5…………

Difference between the first two terms = -1 – 1 = -2

Difference between the third and second term = -3 – (-1) = -2

Difference between the fourth and third term = -5 – (-3) = -2

Since $a_2–a_1=a_3-a_2=a_4-a_3$, this sequence is an AP