If 3 + 5 +7 + ... + upto n terms/5 + 8 + 11 + ... up to terms = 7, then find the value of n.

Question

If \(\frac{3 + 5 +7 + ... + upto\,n\,terms}{5 + 8 + 11 + ... upto\,10\,terms }\) = 7 , then find the value of n.

3 + 5 +7 + ... + upto n terms/5 + 8 + 11 + ... up to terms = 7

Answer 1

Here,

3 + 5 +7 + ... + upto n terms/5 + 8 + 11 + ... up to terms = 7

i.e.,

\(\frac{S_n}{S'_{10}}\) = 7

∴n(2+n) =7×5×37 

∴n²+2n-1295=0 

∴(n-35) (n+37) = 0 

∴ n=35 or n = -37 

Which is not possible as n is non negative. 

So, n = 35