question_answer

How many terms of the A.P. 18, 16, 14, ?. Be so that their sum is zero?

Answer:

Given, A.P is 18, 16, 14??.

We have, \[a=18,\text{ }d=16-18=14-16=-\text{ }2\]

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

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

\[\Rightarrow \,\frac{n}{2}[2\times 18+(n-1)(-2)]=0\]

\[\Rightarrow \,36-2n+2=0\]

\[\Rightarrow \,2n=38\]

\[\therefore \,n=19\]

Hence, the no. of terms are 19.