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.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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answers

rauschg

rauschg · hand

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step-by-step explanation:

you first to choose the points and then move from then as the slope you have