In a geometric progression of positive terms, the 5th term is 9 times the 3rd term and the sum of the 6th and 7th terms is 972. find the
a) common ratio
b) sum of the first 6 terms

a) 3

b) 364

Step-by-step explanation:

A geometric sequence in explicit form is where is the first term and is the common ratio.

We are given:

.

What is a) r?

What is b) the sum of the first 6 terms?

So I'm going to use my first equation and use my explicit form to find those terms in terms of r:

Divide both sides by :

.

So part a is 3.

Now for part b).

We want to find .

So far we have:

.

We also haven't used:

.

I'm going to find these terms in terms of r (r=3).

You have like terms to add:

Divide both sides by 972:

The first term is 1 and the common ratio is 3.

The terms we wrote can be simplify using a substitution for the first term as 1:

.

Now we just need to find the sum of those six terms:

1+3+9+27+81+243=364.

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in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.