Which of the following list of numbers forms an AP?
(i) 4, 4 + √3 , 4 + 2√3, 4 + 3√3, 4 + 4√3
(ii) 0.3, 0.33, 0.333, 0.3333, 0.33333
(iii) 35, 65 , 95 , 125 , 3
(iv) -15 , -15 , -15 , -15 , -15
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 a2–a1 = a3−a2 = a4−a3
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 a2–a1 ≠ a3−a2
This series is not an AP
(iii) 35, 65, 95, 125, 3
Difference between first two consecutive terms = 65–35 = 35
Difference between third and second consecutive terms = 95–65 = 35
Difference between fourth and third consecutive terms = 125 – 95 = 35
Since a2–a1 = a3–a2 = a4–a3
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 a2–a1 = a3–a2 = a4–a3
This series is an AP