Find the 10th term of the geometric sequence whose common ratio is 1/2 and whose 1st term is 2.

Step-by-step explanation:

Geometric sequence means there is a common ratio. All that means is term divided previous term is the same across your sequence.

ONE WAY:

So we are given here that:

and that the first term which is is 2.

This implies after multiplying both sides by 2 and getting that .

So you have that

2,1,...

basically you can just multiply by 1/2 to keep generating more terms of the sequence.

Third term would be .

Fourth term would be .

...keep doing this til you get to the 10th term.

ANOTHER WAY:

Let's make a formula.

is the first term.

is the common ratio.

And we want to figure out what happens at .

Let's plug in our information we have

:

Put into calculator or do by hand...

Scratch work:

.

End scratch work.

The answer is that the tenth term is

For an nth term in a geometric sequence

where n is the number of terms

r is the common ratio

a is the first term

From the question

a = 2

r = 1/2

n = 10

So the 10th term of the sequence is

Hope this helps you

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175