question_answer

If the \[{{10}^{th}}\] term of an A.P. is 52 and the \[{{17}^{th}}\] term is 20 more than the \[{{13}^{th}}\] term, find the A.P.

Answer:

Given, \[{{a}_{10}}=52;{{a}_{17}}={{a}_{13}}+20\]

\[\Rightarrow \]            \[a+16d=a+12d+20\]

\[\Rightarrow \]                 \[16d=12d+20\]

\[\Rightarrow \]                  \[4d=20\]

\[\Rightarrow \]                    \[d=\frac{20}{4}=5\]

Also,                   \[a+9d=52\]

\[\Rightarrow \]           \[a+9\times 5=52\]

\[a+45=52\]

\[a=7\]

Therefore A.P. = 7, 12, 17, 22, 27....