Find the geometric means in the following sequence.

Question

Find the geometric means in the following sequence.

–14,   ?  ,   ?  ,    ?  ,    ?  , –235,298

 

Question 20 options:

98, 686, 4,802, 33,614

–1,960, –2,940, –3,920, –4,900

–98, –686, –4,802, –33,614

–686, –4,802, –33,614, –235,313

Answer 1

Geometric mean = having a common ratio.

The equation for "geometric mean" sequence is a_n = a₁ ⋅ r^n-1, where a_n = nth term in the sequence, a₁ = 1st term in the sequence and r = common ratio.

Let's find the common ratio, since we know a₁ = -14 and a₆ = -235,298.

So -235,298 = -14 ⋅ r^6-1. Divide by -14 on both sides, you get 16807 = r⁵. To "undo" r⁵, you need the 5th root (5√). So 5√(16807) = 7.

Since the common ratio is 7, let's do the math.

-14 * 7 = -98

-98 * 7 = -686

-686 * -4802

-4802 * 7 = -33,614

-33,614 * 7 = -235,298.

And those are the missing values in the sequence.

I hope this helps.