Question

If any odd number of terms are in A.P., then the first, middle & last terms of the series are in

• A. G.P.
• B. H.P.
• C. A.P.
• D. A.G.P.

Answer 1

The correct option is C A.P.

Let the number of terms be $k=2n+1$ where $nϵN$

First term $=a$

Last term $=a+(2n+1-1)d=a+2nd$

Middle term, $(\frac{k+1}{2}{)}^{th}$ term $=(n+1{)}^{th}$ term $=a+nd$
Thus, first, middle and last term are in AP