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

If the sum of the first $n$ even natural numbers is $k$ times the sum of the first $n$ odd natural numbers,then $k = ........$

If the sum of $n$ terms of an arithmetic progression is $3n^2 + 5n$ and $T_m = 164$,then $m = \dots$

If the four angles of a quadrilateral are in an arithmetic progression and their common difference is $10^{\circ}$,what are the measures of the angles of the quadrilateral?

Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10} = 390$ and the ratio of the tenth and the fifth terms is $15:7$,then $S_{15} - S_5$ is equal to:

The interior angles of a polygon are in $A.P.$ If the smallest angle is $120^o$ and the common difference is $5^o$,then the number of sides is

Vedclass Test Series

Exam Paper Generator

Online Exam Module