question_answer

How many terms of the A. P. 65, 60, 55,.... be taken so that their sum is zero?

Answer:

Given, A.P. is 65, 60, 55,....

We have, \[a=65,\text{ }d=60-65=55-60=-5\]

Now, \[{{S}_{n}}=0\]

Therefore,                      \[{{S}_{n}}=\frac{n}{2}[2a+(n-1)d]=0\]

\[\Rightarrow [2(65)+(n-1)(-5)]=0\]

\[\Rightarrow 130-5n+5=0\]

\[\Rightarrow 135-5n=0\]

\[\Rightarrow 5n=135\]

\[\therefore n=27\]

Hence, the no. of terms are \[27\].