Question

Which term of the sequence $(-8+18i)$, $(-6+15i)$, $(-4+12i),.$ Is purely imaginary

• A. $5th$
• B. $7th$
• C. $8th$
• D. $6th$

Answer 1

Answer: (A)

$5th$

$(-8+18i),(-6+15i),(-4+12i)+.....$

This is an AP

with $a=-8+18i$

$d=-6+15i+8-18i=2-3i$

$a+(n-1)d=x+iy$

$(-8+18i)+(n-1)(2-3i)=x+iy$

$-8+18i+2n-3ni-2+3i-x+iy$

$(-10+2n)+(21-3n)i=x+iy$

Given that $x=0$ so that the number can be a imaginary

$-10+2n=0$

$2n=10$

$n=5$

$\therefore 5^{th}$ term is purely imaginary