Three numbers form a g.p.if the first and third numbers are 5 and 245 respectively, find two possible values for the middle number.

9 answers

let the middle number be x

then
x/5 = 245/x
x^2 = 1225
x = ± 35

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To find the middle number in a geometric progression (g.p.), we need to know the common ratio between the numbers. The common ratio (r) is found by dividing any term by its preceding term.

Given that the first number (a₁) is 5 and the third number (a₃) is 245, we can find the common ratio (r) as follows:

r = a₃ / a₁

Substituting the given values:
r = 245 / 5
r = 49

Now that we know the common ratio, we can find the middle number (a₂) by multiplying the first term (a₁) by the common ratio (r).

If a₁ = 5 and r = 49, then:
a₂ = a₁ * r
a₂ = 5 * 49
a₂ = 245

Therefore, one possible value for the middle number is 245.

To find another possible value, we can use a negative common ratio (-r).

If a₁ = 5 and r = -49, then:
a₂ = a₁ * r
a₂ = 5 * (-49)
a₂ = -245

Therefore, another possible value for the middle number is -245.

In conclusion, the two possible values for the middle number in the given g.p. are 245 and -245.