Question

The values of x for which the numbers -2/3,x,-27/2 are in GP​

Answer 1

Given : -2/3 , x , -27/2 are in GP

To find : Value of x

Solution :

GP is a sequence of numbers in which common ratio between two consecutive terms is always constant throughout the whole sequence.

Common ratio = a2 / a1 = a3 / a2 ( Or any two consecutive terms )

Here,

• a1 = First term of GP
• a2 = Second term of GP
• a3 = Third term of GP

Since we already discussed above that common ratio remains same. So,

=> r = (-27 / 2) ÷ x = x ÷ ( -2 / 3 )

=> (-27 / 2) ÷ x = x ÷ ( -2 / 3 )

=> -27 / 2 × -2 / 3 = x²

=> 9 = x²

=> ± 3 = x

Hence the value of x must be +3 or -3 for the given terms to be the member of a geometric sequence.

Answer 2

Step-by-step explanation:

x = +3 and -3

Hope it helps

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