question_answer

Find the middle term of the A.P. 213, 205, 197, ......., 37.

Answer:

Given A.P. is 213, 205, 197, .........., 37

Here

Let n be the number of terms

Then,                \[{{T}_{n}}=a+(n-1)d\]

\[37=213+(n-1)(-8)\]

\[37=213-8n+8\]

\[8n=184\]

\[n=23\]

And middle term is \[\frac{{{(n+1)}^{th}}}{2}\] term i.e. 12th term

\[\therefore {{T}_{12}}=213+(12-1)(-8)\]

\[=213+11(-8)\]

\[=213-88\]

\[\therefore {{T}_{12}}=125\]

\[\therefore \] Middle term of the A.P. is \[125\].