MathematicsState True/False.The first term, common difference and fifth term of an A.P. . −1, −5 6 , −2 3 , −1 2 ,… are respectively −1,  1 6 ,  and −1 3 .

State True/False.


The first term, common difference and fifth term of an A.P. . 1, 5 6 , 2 3 , 1 2 , are respectively 1,  1 6 ,  and 1 3 .


  1. A
    True
  2. B
    False  

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    Solution:

    Given A.P. is 1, 5 6 , 2 3 , 1 2 ,
    So, first term: t 1 =1 , second term: t 2 = 5 6 , third term: t 3 = 2 3 , fourth term: t 4 = 1 2 /  Applying formula and determining the value of common difference:
    d= t 2 t 1 d= 5 6 (1) = 5 6 +1 = 1 6
    Determining next term of A.P.:
    t 5 = t 4 +d
    t 5 = 1 2 +d t 5 = 1 2 + 1 6 = 3+1 6 t 5 = 2 6 = 1 3
    Therefore, the first term t 1 is -1, common difference(d) is 1 6 and the fifth term is 1 3 . Thus, the given statement is true.
    Hence, option (1) is correct.
     
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