Establish the relationship between the first and ‘n’th term of an

1.	Establish the relationship between the first and ‘n’th term of an A.P. in which ‘d’ = 0.
Answer» Let the first term of that A.P. is ‘a’. Then common difference (d) = 0 given then nth term = a + (n – 1) d = a + (n – 1) (0) = a + 0 = a ∴ a_n = a So, when d = 0 is given the ‘n’ th term of an A.P. (a_n) is equal to its first term (a).

Establish the relationship between the first and ‘n’th term of an A.P. in which ‘d’ = 0.

Answer»

Let the first term of that A.P. is ‘a’.

Then common difference (d) = 0 given then nth term = a + (n – 1) d

= a + (n – 1) (0)

= a + 0 = a

∴ a_n = a

So, when d = 0 is given the ‘n’ th term of an A.P. (a_n) is equal to its first term (a).