Q. 224.5( 2 Votes )

The sum of the fi

Answer :

Given sum of first seven terms of AP, S7 = 182.


We know that sum of first n terms of AP, Sn = (n/2) [2a + (n – 1) d]


182 = (7/2) [2a + (7 – 1) d]


182 = (7/2) [2a + 6d]


182 = (7/2) (2) [a + 3d]


182/7 = a + 3d


a + 3d = 26 … (1)


Also given the 4th and 17th terms are in the ratio 1: 5.


We know that nth term, an = a + (n – 1) d


a4 = a + (4 – 1) d = a + 3d


a17 = a + (17 – 1) d = a + 16d


(a + 3d)/ (a + 16d) = 1/5


5 (a + 3d) = 1 (a + 16d)


5a + 15d = a + 16d


4a = d … (2)


Substituting the above in (1),


a + 3 (4a) = 26


a + 12a = 26


13a = 26


a = 2


Substituting a = 2 in (2),


d = 8


The AP will be as follows: 2, 10, 18, 26, …


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