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. $\left\{9-8i, 8-6i, -4i, \ldots\right\}$
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