Consider the sequence 8 A +2 B , 6 A + B , 4 A , 2 A - B , ldots ldots . .. Which term of this sequence will have a coefficient of A which is twice the coefficient of B?

Question

Consider the sequence 8 A +2 B , 6 A + B , 4 A , 2 A - B , ldots ldots . .. Which term of this sequence will have a coefficient of A which is twice the coefficient of B? (A) 10 text th  (B) 14 text th  (C) 17 text th  (D) none

Tardigrade Admin · Accepted Answer

Coefficient of A in n text th text term =8+(n-1)(-2) =10-2 n text coefficient of B text in n text th text term =2+(n-1)(-1) =3-n 10-2 n=2(3-n) ⇒ 10=6 text which is absurd ⇒ text none

Q. Consider the sequence $8 A + 2 B, 6 A + B, 4 A, 2 A - B, \dots\dots ..$ . Which term of this sequence will have a coefficient of A which is twice the coefficient of B?

$1 0^{th}$

$1 4^{th}$

$1 7^{th}$

none

Coefficient of A in $n^{th} term = 8 + (n - 1) (- 2)$
$= 10 - 2 n$
$coefficient of B in n^{th} term = 2 + (n - 1) (- 1)$
$= 3 - n$
$10 - 2 n = 2 (3 - n) \Rightarrow 10 = 6$
$which is absurd \Rightarrow none$

Q. Consider the sequence 8A+2B,6A+B,4A,2A−B,……... Which term of this sequence will have a coefficient of A which is twice the coefficient of B?

10th

14th

17th