Find the geometric means in the following sequence. –14, ? , ? , ? , ? , –235,298

Question

asked May 21, 2021 124k views

2 Answers

Zhazha · Answer 1 · 2021-05-26T09:15:17+0000

Answer:

The geometric mean of the sequence is 1814.99.

Explanation:

The formula to compute the geometric mean is:

$GM=\sqrt[n]{a_(1)\cdot a_(2)\cdot a_(3)\cdot...a_(n)}$

The geometric sequence is:

–14, ? , ? , ? , ? , –235,298

The nth term of a geometric sequence is:

$a_(n)=a_(1)\cdot r^(n-1)$

Here, r is the common ratio.

There are 6 terms in the sequence provided.

Compute the common ratio as follows:

$a_(6)=a_(1)\cdot r^(6-1)\\\\-235298=-14* r^(5)\\\\r=[(235298)/(14)]^(1/5)\\\\r=7$

Thus, the common ratio is 7.

The missing terms are:

$a_(2)=a_(1)\cdot r^(2-1)\\=-14* 7\\=-98$

$a_(3)=a_(1)\cdot r^(3-1)\\=-14* 7^(2)\\=-686$

$a_(4)=a_(1)\cdot r^(4-1)\\=-14* 7^(3)\\=-4802$

$a_(5)=a_(1)\cdot r^(5-1)\\=-14* 7^(4)\\=-33,614$

Compute the geometric mean as follows:

$GM=\sqrt[n]{a_(1)\cdot a_(2)\cdot a_(3)\cdot...a_(n)}$

$=\sqrt[6]{-14* -98* -686* -4802*-33614* -235298} \\\\=1814.9854\\\\\approx 1814.99$

Thus, the geometric mean of the sequence is 1814.99.