1.

Find the indicated terms of the sequence whose nth terms are: An = (n - 1)(2-n)(3-n); a1,a2,a3​

Answer»

ANSWER:

  1. a_{1} = 0
  2. a_{2} =0
  3. a_{<klux>3</klux>} = 0

Explanation:

GIVEN:

  • The nth term of an A.P. = a_{n} = (n - 1)(2-n)(3-n)

To find:

a1, a2 & a3​

Proof:

a_{n} = (n - 1) (2-n) (3-n)

  1. Putting n= 1 we get:

      = a_{1} = (1-1) (2-1) (3-1)

      ⇒ a_{1} = (0) (1) (2)

      ⇒ a_{1} = 0

HENCE, first term = a_{1} = 0

     2. Putting n= 2 we get:

     = a_{2} = (2-1) (2-2) (3-2)

     ⇒  a_{2} = ( 1 ) (0) (1)

     ⇒ a_{2} =0

Hence, second term = a_{2} =0

     3. Putting n= 3 we get:

     = a_{3} = ( 3-1) (2-3) (3-3)

     ⇒ a_{3} =  (2) (-1) (0)

     ⇒ a_{3} = 0

Hence, THIRD term = a_{3} = 0

  • Thus, the indicated terms of the sequence are respectively:
  1. a_{1} = 0
  2. a_{2} =0
  3. a_{3} = 0

Hope you got that.

Thank You.



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