Question

Which of these are arithmetic progressions and why?

a) 2, 3, 5, 7, 8, 10, 15, ……

b) 2, 5, 7, 10, 12, 15 ……

c) -1,-3,-5,-7, ……

Answer 1

a) 2, 3, 5, 7, 8, 10, 15, …… is not an A.P. 

∵ a₂ – a₁ = 3 – 2 = 1 

a₃ – a₂ = 5 – 3 = 2 

a₄ – a₃ = 7 – 5 = 2 

i.e., The difference between any two successive terms is not same throughout the series. 

(or) 

Every number is not formed by adding a fixed number to its preceding term.

b) The given list does not form an A.P, since each term is not obtained by adding a fixed number to its preceding term.

c) -1,-3,-5,-7,….. is an A.P. 

a₂ – a₁ = – 3 – (- 1) = -3 + 1 = -2 

a₃ – a₂ = – 5 – (-3) = -5 + 3 = -2 

a₄ – a₃ = – 7 – (- 5) = -7 + 5 = -2 

Every number is formed by adding a fixed number to its preceding term,