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The sum of first six terms of an arithme...

The sum of first six terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1:3. Calculate the first and the thirteenth term of the A.P.

Text Solution

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Let the first term and common difference of A.P. be 'a' and 'd' respectively.
Given that, `(a_(10))/(a_(30))=(1)/(3)`
`rArr (a+9d)/(a+29d)=(1)/(3)`
`rArr 3a+27d=a+29d`
`rArr 2a=2d`
`rArr a=d " " `...(1)
and `S_(6)=42`
`rArr (6)/(2)(2a+5d)=42`
`rArr 3(2d+5d)=42 " " `[from (1) ]
`rArr d=2`
`:. a=2`
Now, `a_(13)=a+12d=2+12xx2=26`
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