(Q1).Which of these are arithmetic progressions and why?

(a) 2, 3, 5, 7, 8, 10, 15, ……

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

∵ a2 – a1 = =

a3 – a2 = =

a4 – a3 = =

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

(b) 2, 5, 7, 10, 12, 15 ……

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

(c) -1,-3,-5,-7, ……

-1,-3,-5,-7,….. is an A.P.

a2 – a1 = – – (- ) = - + = -

a3 – a2 = – – (-) = - + = -

a4 – a3 = – – (- ) = - + = -

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