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Question

Which of the following list of numbers forms an AP?
(i) 4, 4 + 3 , 4 + 23, 4 + 33, 4 + 43

(ii) 0.3, 0.33, 0.333, 0.3333, 0.33333

(iii) 35, 65 , 95 , 125 , 3

(iv) -15 , -15 , -15 , -15 , -15


A

Only (i) and (ii)

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B

Only (ii) and (iii)

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C

Only (iii) and (iv)

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D

Only (i), (iii) and (iv)

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Solution

The correct option is D

Only (i), (iii) and (iv)


Consider each series
(i) 4, 4 + 3, 4 + 2 3, 4 + 3 3, 4 + 4 3

Difference between first two consecutive terms = 4 + 3 - 4 = 3

Difference between third and second consecutive terms = 4 + 2 3 - 4 + 3 = 3

Difference between fourth and third consecutive terms = 4 + 3 3– 4 + 2 3 = 3

Since a2a1 = a3a2 = a4a3

This series is an AP

(ii) 0.3, 0.33, 0.333, 0.3333, 0.33333

Difference between first two consecutive terms = 0.33 - 0.3 = 0.03

Difference between third and second consecutive terms = 0.333 - 0.33 = 0.003

Since a2a1 a3a2
This series is not an AP

(iii) 35, 65, 95, 125, 3

Difference between first two consecutive terms = 6535 = 35

Difference between third and second consecutive terms = 9565 = 35

Difference between fourth and third consecutive terms = 12595 = 35

Since a2a1 = a3a2 = a4a3
This series is an AP

(iv) -15, -15, -15, -15, -15

Difference between first two consecutive terms = -15 – (- 15) = 0

Difference between third and second consecutive terms = -15 – (-15) = 0

Difference between fourth and third consecutive terms = -15 – (-15) = 0

Since a2a1 = a3a2 = a4a3
This series is an AP


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