question_answer

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

A)  4th                               

B)  5th     

C)  6th                               

D)  7th

Correct Answer: B

Solution :

(b): Let a be the first term and d the common difference of an AP. Also, let kth term of AP be zero. \[\therefore {{a}_{k}}=a+(k-1)d\,\,\therefore {{a}_{3}}=a+2d=4\]                      \[[\because {{a}_{3}}=4(given)]......(i)\] And                                          \[[\because {{a}_{9}}=-8(given)]......(ii)\] On subtracting Eq. (i) from Eq. (ii), we get \[6d=-12\Rightarrow d=\frac{-12}{6}=-2\] \[\therefore \] From Eq. (i), \[a+2\times (-2)=4\] \[\Rightarrow a-4=4\,\,\,\,\Rightarrow a=4+4=8\] kth term: \[{{a}_{k}}=0\Rightarrow a+(k-1)d=0\,\,\] \[\Rightarrow 8+(k-1)(-2)=8\,\,\,\Rightarrow (k-1)(-2)=-8\] \[\Rightarrow k-1=\frac{-8}{-2}=4\]\[\Rightarrow k=4+1=5\] Hence, 5th term of this AP is zero.