Question

The number of terms in an A.P. whose first term is 10, last term is 50 and the sum of all terms is 300, is ___________.

Answer 1

First term of A.P is given = 10
Last term of A.P is given = 50
Sum of all terms S_n = 300 (given)
Since sum of all terms $S_n=\frac{n\left(\mathrm{First}\mathrm{term}+\mathrm{Last}\mathrm{term}\right)}{2}$
$$\begin{gathered} \mathrm{i}.\mathrm{e}300=n{\left(\frac{10+50}{2}\right)}^2 \\ \mathrm{i}.\mathrm{e}300=n\left(\frac{60}{2}\right) \\ \mathrm{i}.\mathrm{e}300=n\left(30\right) \\ \mathrm{i}.\mathrm{e}n=10 \end{gathered}$$
Hence, number of terms of an A.P is 10.