Question

Which term of the sequence $8-6i,7-4i,6-2i$,... is purely real ?

• A. $10$
• B. $12$
• C. $9$
• D. $4$

Answer 1

Answer: (D)

$4$

The given sequence is an A.P. with first term $a=8-6i$ and common difference $d=-1+2i$. The nth term of the given A.P. is given by :

$a_n=a+(n-1)d=8-6i+(n-1)(-1+2i)=(9-n)+i(2n-8)$

Let the nth term of the sequence is purely real.

Therefore,

$(9-n)+i(2n-8)$ is purely real.

$2n-8=0$

$n=4$

So, 4th term of the sequence is purely real.