question_answer

If the ratio of the sum of the first n terms of two A.P.s is \[(7n+1):(4n+27)\], then find the ratio of their 9th terms.

Answer:

Ratio of sum of first n terms of two A.P.s are

\[\frac{\frac{n}{2}\left[ 2a+(n-1)d \right]}{\frac{n}{2}\left[ 2A+(n-1)D \right]}=\frac{7n+1}{4n+27}\]

Put                   \[n=17\]

\[\Rightarrow \]               \[\frac{2a+(16)d}{2A+(16)D}=\frac{120}{95}\]

\[\frac{2a+(16)d}{2A+(16)D}=\frac{120}{95}=\frac{24}{19}\]

\[\frac{a+8d}{A+8D}=\frac{24}{19}\]

Hence ratio of 9th terms of two A.Rs is \[24:19\]