Q. 124.3( 12 Votes )

The sum of first

Answer :

If 'a' is the first term and 'd' is the common difference in an AP,


We know that,


nth term of an AP, an = a + (n - 1)d


Sum of first 'n' terms of an AP,


Now, given


Sum of first six terms, S6 = 42



3[2a + 5d] = 42


2a + 5d = 14 …[1]


Also, given ratio of 10th and 30th term is 1 : 3




3a + 27d = a + 29d


2a = 2d


a = d


Putting d = a in [1]


2a + 5a = 14


7a = 14


a = 2


i.e. First term of AP is 2.


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