Which term of the sequence (-8 + 18i), (-6 + | vedclass

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(A) The given sequence is an Arithmetic Progression $(AP)$ where the first term $a = -8 + 18i$ and the common difference $d = (-6 + 15i) - (-8 + 18i)

Vedclass · Accepted Answer

$5$

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(A) The given sequence is an Arithmetic Progression $(AP)$ where the first term $a = -8 + 18i$ and the common difference $d = (-6 + 15i) - (-8 + 18i) = 2 - 3i$.The $n^{th}$ term of an $AP$ is given by $T_n = a + (n - 1)d$.$T_n = (-8 + 18i) + (n - 1)(2 - 3i)$$T_n = -8 + 18i + 2n - 2 - 3ni + 3i$$T_n = (-10 + 2n) + i(21 - 3n)$For the term to be purely imaginary,the real part must be zero:$-10 + 2n = 0$$2n = 10$$n = 5$Thus,the $5^{th}$ term is purely imaginary.

Which term of the sequence $(-8 + 18i), (-6 + 15i), (-4 + 12i), \dots$ is purely imaginary (in $^{th}$)?

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