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.

Explanation

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`