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The sum of first six terms of an A.P. is...

The sum of first six terms of an A.P. is 42. The ratio of its 10th term to its 30th term is 1:3. Find the first term of the A.P.

Text Solution

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Let `a` is the first term and `d` is the common difference.
`:. S_6 = 6/2(2a+(6-1)d) = 42`
`=>2a+5d = 14->(1)`
Also, `a_10/a_30 = (a+9d)/(a+29d) = 1/3`
`=> 3a+27d = a+29d`
`=>2a = 2d=> a= d`
From (1),
`2a+5a = 14=>7a = 14=> a= 2`
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