MathematicsIf the n th   term of an A.P. is (2n+1)  , then the sum of its first three terms is ____.

If the n th   term of an A.P. is (2n+1)  , then the sum of its first three terms is ____.


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    Solution:

    If the n th   term of an A.P. is (2n+1)  , then the sum of its first three terms is 15.
    Here,
    We have been given,
    t n =2n+1  
    a= t 1 =2(1)+1=3   t 2 =2(2)+1=5  
    d= t 2 t 1  
    d=53=2  
    We know that,
    S n = n 2 [2a+(n1)d] S 3 = 3 2 [2(3)+(31)2] S 3 = 3 2 [6+(2)2] S 3 = 3 2 [6+4] S 3 = 3 2 [10] S 3 =3(5) S 3 =15  
    Therefore, the sum is 15.
     
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