Question

if 5/2, p, 2/5 are in gp. then the value of p is 1.do you agree? justify your answer?​

Answer 1

Answer:

yes,p=1

Step-by-step explanation:

because it satisfies the condition for being gp

Answer 2

$\pink { I \: disagree . }$

Reason :

$We \: know \: that,$

A Geometric Progression (GP) is a list of numbers in which each term is obtained by multiplying preceding term with a fixed number 'r' except first term. This fixed number is called Common ratio 'r'.

$Given \: \frac{5}{2},p , \frac{2}{5} \: are \: in \: G.P$

$\implies \frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}}$

$\implies \frac{p}{\frac{5}{2}}= \frac{\frac{2}{5}}{p}$

$\implies p^{2} = \frac{2}{5} \times \frac{5}{2}$

$\implies p^{2} = 1$

$\implies p = \pm \sqrt{1}$

$\implies p = \pm 1$

Therefore.,

$\red{ Value \: of \: p } \green { = \pm 1}$

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