# The geometric mean between the first two terms in a geometric sequence is 32.If third term is 4,fin the first term

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If we let x be the first term, y be the second term, and r be the common ratio (that number which we multiply to x to get y, and also the number we multiply to y to get 4, which is the third term), then we get

We also know that

We now have a system of three equations, and three unknowns.

Solving for r gives us

Substituting this in the first equation for x gives

Which, when solved, gives

Thus, since yr = 4, we can deduce that

Finally, since xr = y, then xr = 16, and