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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$5$

Vedclass · Answer

(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 $^{th}$)?

Similar Questions

Find the sum of integers from $1$ to $100$ that are divisible by $2$ or $5.$

If for an arithmetic progression $S_{2n} = 2S_n$,then $S_{3n} / S_n = \dots$

If the $9^{th}$ term of an $A.P.$ is $35$ and the $19^{th}$ term is $75$,then its $20^{th}$ term will be:

Find the mean of the first $n$ terms of the $A$.$P$. $a, (a + d), (a + 2d), \dots$

Write the first five terms of the sequence whose $n^{th}$ term is $a_{n} = \frac{2n - 3}{6}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module