Question

Which term of the sequence $\{9-8i,8-6i,7-4i,....\}$ is a real number?

• A. $4^{th}$ term
• B. $5^{th}$ term
• C. $6^{th}$ term
• D. $7^{th}$ term

Answer 1

Answer: (B)

We have an A.P. $\left\{9-8i,8-6i,-4i,\dots \right\}$
Here, first term, $a=9-8i$
And common difference, $d=8-6i-9+8i$
$=-1+2i$
Let $r^{th}$ term be real number.
$T_r=a+\left(r-1\right)d=9-8i+\left(r-1\right)\left(-1+2i\right)$
$=9-8i-r+1+2ir-2i$
$=10-r+i\left(2r-10\right)$
since, $T_r$ is real,
$\therefore 2r-10=0$
$\Rightarrow r=5$
Thus, $5^{th}$ term is a real number