In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

Question

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals (A) (1/2)(1-√5) (B) (1/2)√5 (C) √5 (D) (1/2)(√5-1)

Tardigrade Admin · Accepted Answer

Given arnâ1 = arn + arn+1 ⇒ 1=r+r2 ∴ r=(√5-1/2).

Q. In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

$\frac{1}{2} (1 - 5)$

$\frac{1}{2} 5$

$5$

$\frac{1}{2} (5 - 1)$

Given $a r^{n - 1} = a r^{n} + a r^{n + 1}$
$\Rightarrow 1 = r + r^{2}$
$∴ r = \frac{5 - 1}{2} .$

Q. In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

21​(1−5​)

21​5​

5​

21​(5​−1)

Given arn−1=arn+arn+1 ⇒1=r+r2 ∴r=25​−1​.

$\frac{1}{2} (1 - 5)$

$\frac{1}{2} 5$

$5$

$\frac{1}{2} (5 - 1)$

Given $a r^{n - 1} = a r^{n} + a r^{n + 1}$
$\Rightarrow 1 = r + r^{2}$
$∴ r = \frac{5 - 1}{2} .$