Which term of the sequence `12+8i ,\ 11+6i ,\ 10+4i ,...` is (a) purely real and (b). purely imaginary?

Explanation

We have, `12+8i, 11+6i, 10+4i`

Let n th term is purely imaginary,

`T_n`​ `=a+(n−1)d`
and

`a=12+8i`

`d=11+6i−(12+8i)`

`=−1−2i`

So,`T_n``​ =12+8i+(n−1)(−1+2i)`
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