Which of these are arithmetic progressions and why?a) 2, 3, 5, 7, 8, 1

1.	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» 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,

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»

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,