Question

if the terms 7,a,a,63 are in proportion, then a is 7:3​

Answer 1

SOLUTION

GIVEN

The terms 7,a,a,63 are in proportion

TO DETERMINE

The value of a

EVALUATION

Here it is given that the terms 7,a,a,63 are in proportion

So by the given condition

7 : a = a : 63

$\displaystyle \sf{ \frac{7}{a} = \frac{a}{63} }$

$\displaystyle \sf{ \implies \: {a}^{2} = 7 \times 63 }$

$\displaystyle \sf{ \implies \: {a}^{2} = 7 \times 7 \times 3 \times 3 }$

$\displaystyle \sf{ \implies \: a = \pm \: (7 \times 3) }$

$\displaystyle \sf{ \implies \: a = \pm \: 21}$

FINAL ANSWER

The required value of a = - 3 or 3

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