Let a

Question

Let a < b < c be three integers such that a, b, c is an arithmetic progression and a, c, b is a geometric progression, then find the smallest positive value of c (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5987800a86c3e9f30b431bf8e61bc39e-.png" /> (A+d)2=(A-d) A A2+d2+2 A d=A2-A d d2=-3 A d d=0, d=-3 A c=A+d=-2 A ∴ c min =2 .

Q. Let $a < b < c$ be three integers such that $a, b, c$ is an arithmetic progression and $a, c, b$ is a geometric progression, then find the smallest positive value of c

$(A + d)^{2} = (A - d) A$
$A^{2} + d^{2} + 2 A d = A^{2} - A d$
$d^{2} = - 3 A d$
$d = 0, d = - 3 A$
$c = A + d = - 2 A$
$∴ c_{m i n} = 2.$

Q. Let a<b<c be three integers such that a,b,c is an arithmetic progression and a,c,b is a geometric progression, then find the smallest positive value of c

(A+d)2=(A−d)A A2+d2+2Ad=A2−Ad d2=−3Ad d=0,d=−3A c=A+d=−2A ∴cmin​=2.

Q. Let $a < b < c$ be three integers such that $a, b, c$ is an arithmetic progression and $a, c, b$ is a geometric progression, then find the smallest positive value of c

$(A + d)^{2} = (A - d) A$
$A^{2} + d^{2} + 2 A d = A^{2} - A d$
$d^{2} = - 3 A d$
$d = 0, d = - 3 A$
$c = A + d = - 2 A$
$∴ c_{m i n} = 2.$