# The number of terms in an A.P. whose first term is 10,

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 ___________.

Solution:

First term of A.P is given  = 10

Last term of A.P is given = 50

Sum of all terms Sn = 300        (given)

Since sum of all terms $S_{n}=\frac{n \text { (First term+Last term) }}{2}$

i. e $300=n\left(\frac{10+50}{2}\right)^{2}$

i. e $300=n\left(\frac{60}{2}\right)$

i. e $300=n(30)$

i. e $n=10$

Hence, number of terms of an A.P is 10.