Q : 9      If the \small 3rd and the \small 9th terms of an AP are \small 4  and  \small -8  respectively, which term of this AP is zero?
 

Answers (1)

It is given that
\small 3rd and the \small 9th terms of an AP are \small 4  and  \small -8  respectively
Now,
a_3 = 4=a+2d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -(i)
And
a_{9} = -8=a+8d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -(ii)
On solving equation (i) and (ii) we will get 
a= 8 \ \ \ and \ \ \ d = -2
Now,
Let nth term of given AP is 0
Then,
a_{n} = a+(n-1)d
0 = 8+(n-1)(-2)
2n = 8+2= 10
n = \frac{10}{2} = 5
Therefore, 5th term of given AP is 0

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