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The sum of first six terms of an arithmetic progression is

   

. The ratio of the

   

term to the

   

term is

   

. Calculate the first and the thirteenth term.
contexto.140

Given,

   

We know that,

   

So, we have

   

   

… (i) [Dividing by

   

]

And,

   

On cross-multiplication, we have

   

Using the above the relation in (i), we get

   

Hence, the first term of the A.P is

   

.

Now, the thirteenth term is given by