Let A 1, A 2, A 3, ldots ldots be an increasing geometric progression of positive real numbers. If A 1 A 3 A 5 A 7=(1/1296) and A 2+ A 4=(7/36), then, the value of A 6+ A 8+ A 10 is equal to

Question

Let A 1, A 2, A 3, ldots ldots be an increasing geometric progression of positive real numbers. If A 1 A 3 A 5 A 7=(1/1296) and A 2+ A 4=(7/36), then, the value of A 6+ A 8+ A 10 is equal to (A) 33 (B) 37 (C) 43 (D) 47

Tardigrade Admin · Accepted Answer

A 1 ⋅ A 3 ⋅ A 5 ⋅ A 7=(1/1296) ( A 4)4=(1/1296) A 4=(1/6) ...(1) A 2+ A 4=(7/36) A 2=(1/36) ...(2) A 6=1 A 8=6 A 10=36 A 6+ A 8+ A 10=43

Q. Let $A_{1}, A_{2}, A_{3}, \dots\dots$ be an increasing geometric progression of positive real numbers. If $A_{1} A_{3} A_{5} A_{7} = \frac{1}{1296}$ and $A_{2} + A_{4} = \frac{7}{36}$ , then, the value of $A_{6} + A_{8} + A_{10}$ is equal to

33

37

43

47

$A_{1} \cdot A_{3} \cdot A_{5} \cdot A_{7} = \frac{1}{1296}$
$(A_{4})^{4} = \frac{1}{1296}$
$A_{4} = \frac{1}{6}$ ...(1)
$A_{2} + A_{4} = \frac{7}{36}$
$A_{2} = \frac{1}{36}$ ...(2)
$A_{6} = 1$
$A_{8} = 6$
$A_{10} = 36$
$A_{6} + A_{8} + A_{10} = 43$

Q. Let A1​,A2​,A3​,…… be an increasing geometric progression of positive real numbers. If A1​A3​A5​A7​=12961​ and A2​+A4​=367​, then, the value of A6​+A8​+A10​ is equal to

33

37

43

47

A1​⋅A3​⋅A5​⋅A7​=12961​ (A4​)4=12961​ A4​=61​ ...(1) A2​+A4​=367​ A2​=361​ ...(2) A6​=1 A8​=6 A10​=36 A6​+A8​+A10​=43

Q. Let $A_{1}, A_{2}, A_{3}, \dots\dots$ be an increasing geometric progression of positive real numbers. If $A_{1} A_{3} A_{5} A_{7} = \frac{1}{1296}$ and $A_{2} + A_{4} = \frac{7}{36}$ , then, the value of $A_{6} + A_{8} + A_{10}$ is equal to

$A_{1} \cdot A_{3} \cdot A_{5} \cdot A_{7} = \frac{1}{1296}$
$(A_{4})^{4} = \frac{1}{1296}$
$A_{4} = \frac{1}{6}$ ...(1)
$A_{2} + A_{4} = \frac{7}{36}$
$A_{2} = \frac{1}{36}$ ...(2)
$A_{6} = 1$
$A_{8} = 6$
$A_{10} = 36$
$A_{6} + A_{8} + A_{10} = 43$