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Question

Which of the following sequences are APs?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11……..

(iii) -1, -1.25, -1.5, -1.75…….

(iv) 1, -1, -3, -5, -7…………


A

(iii) and (iv)

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B

(ii) and (iv)

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C

(i) and (iv)

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D

(i), (iii) and (iv)

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Solution

The correct option is A

(iii) and (iv)


Consider each of the sequences.
(i) 2, 4, 8, 16……..

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

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

Since a2a1a3a2, this sequence is not an AP.

(ii) 2, 3, 5, 7, 11……..

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

Difference of the third and second terms = 5 - 3 = 2

Since a2a1a3a2, this sequence is not an AP.

(iii) -1, -1.25, -1.5, -1.75…….

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

Difference of the third and second terms = -1.5 – (-1.25) = -0.25

Difference of the fourth and third terms = -1.75 – (-1.5) = -0.25

Since a2a1=a3a2=a4a3, this sequence is an AP.

(iv) 1, -1, -3, -5, -7…………

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

Difference of the third and second terms = -3 – (-1) = -2

Difference of the fourth and third terms = -5 – (-3) = -2

Since a2a1=a3a2=a4a3, this sequence is an AP.


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