Question

Which term of the sequence `8-6i ,7-4i ,6-2i , ` is (i) purely real (ii) purely imaginary?

Answer 1

`a=8-6i`
`d=7-4i-8+6i`
`=-1+2i`
`a_n=a+(n-1)d`
`a+ib=8-6i+(n-1)(-1+2i)`
`a+ib=8-6i+(-1)(n-1)+(n-1)2i`
`-6+2(n-1)=0`
`2(n-1)=6`
`n=4`
`a_n=8-6i+(4-1)(-1+2i)`
`=8-6i-3+6i=5`
`4^(th)` term=5
`8+(-1)(n-1)=0`
`8=n-1`
`n=9`
`a_n=8-6i+(9-1)(-1+2i)`
`=8-6i+8(-1+2i)`
`=8-6i-8+16i=10i`
Purely imaginary `9^(th)` term=10i.