Find the sum of the first 7 terms of the following sequence 3,-5,25/3 Round to the nearest hundredth if necessary.

Mathematics

1 answer:

Mademuasel [1]2 years ago

4 0

This is a geometric sequence with first term 3 and a common ratio of -5/3.

Using the sum of a geometric series formula,

$\frac{3(1-(-5/3)^{7}}{1-(-5/3)} \approx \boxed{41.31}$

You might be interested in

A cup of coffee contains 130mg of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how long will it

uysha [10]

It will take approx.65 of caffeine remaining after 6 hours

4 0

3 years ago

I need help with this geometry assignment. Please help.

zvonat [6]

SA = LH + LW + WH + 2(1/2LH)
SA = 4*2 + 5*2 + 3*2 + 2*1/2*4*3
SA = 8 + 10 + 6 + 12
SA = 36

6 0

1 year ago

Change the subject of the formula L = v 4kt - p to k.

Romashka [77]

Answer:

$\boxed{k = \frac{L^2 + p}{4t}}$

General Formulas and Concepts:

Algebra I

Basic Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle L = \sqrt{4kt - p}$

Step 2: Solve for k
We can use equality properties to help us rewrite the equation to get k as our subject:

Let's first square both sides:

$\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\\end{aligned}$

Next, add p to both sides:

$\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\& \rightarrow L^2 + p = 4kt \\\end{aligned}$

Next, divide 4t by both sides:

$\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\& \rightarrow L^2 + p = 4kt \\& \rightarrow \frac{L^2 + p}{4t} = k \\\end{aligned}$