15 results

series - the cumulative sum of a given sequence of terms

100, 75, 50, 25, 0, -25 What is the next number? What is the 100th term?

100, 75, 50, 25, 0, -25 What is the next number? What is the 100th term?
Using point slope, we get (1, 100)(2, 75)
Our [URL='https://www.mathcelebrity.com/search.php?q=%281%2C+100%29%282%2C+75%29&x=0&y=0']series function becomes[/URL]
f(n) = -25n + 125
The next term is the 7th term:
f(7) = -25(7) + 125
f(7) = -175 + 125
f(7) = [B]-50
[/B]
The 100th term is found by n = 100:
f(100) = -25(100) + 125
f(100) = -2500 + 125
f(100) = [B]-2375[/B]

5, 14, 23, 32, 41....1895 What term is the number 1895?

5, 14, 23, 32, 41....1895 What term is the number 1895?
Set up a point slope for the first 2 points:
(1, 5)(2, 14)
Using [URL='https://www.mathcelebrity.com/search.php?q=%281%2C+5%29%282%2C+14%29&x=0&y=0']point slope formula, our series function[/URL] is:
f(n) = 9n - 4
To find what term 1895 is, we set 9n - 4 = 1895 and solve for n:
9n - 4 = 1895
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=9n-4%3D1895&pl=Solve']equation solver[/URL], we get:
n = [B]211[/B]

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended. What is the maximum number of events someone can attend for a total cost of $47?
Subtract the join fee from the total cost:
$47 - $16 = $31
Now divide this number by the cost per event:
$31 / $1 = [B]31 events[/B]

Annie got a new video game. She scored 152 points on the first level, 170 points on the second level

Annie got a new video game. She scored 152 points on the first level, 170 points on the second level, 188 points on the third level, and 206 points on the fourth level. What kind of sequence is this?
This is an [URL='https://www.mathcelebrity.com/sequenceag.php?num=152%2C170%2C188%2C206&n=10&pl=Calculate+Series&a1=&d=']arithmetic series as seen on our calculator[/URL]:

Arithmetic and Geometric and Harmonic Sequences

Free Arithmetic and Geometric and Harmonic Sequences Calculator - This will take an arithmetic series or geometric series or harmonic series, and an optional amount (n), and determine the following information about the sequence

1) Explicit Formula

2) The remaining terms of the sequence up to (n)

3) The sum of the first (n) terms of the sequence Also known as arithmetic sequence, geometric sequence, and harmonic sequence

1) Explicit Formula

2) The remaining terms of the sequence up to (n)

3) The sum of the first (n) terms of the sequence Also known as arithmetic sequence, geometric sequence, and harmonic sequence

DeAndre is a spelunker (someone who explores caves). One day DeAndre is exploring a cave that has a

DeAndre is a spelunker (someone who explores caves). One day DeAndre is exploring a cave that has a series of ladders going down into the depths. Every ladder is exactly 10 feet tall, and there is no other way to descend or ascend (the other paths in the cave are flat). DeAndre starts at 186 feet in altitude, and reaches a maximum depth of 86 feet in altitude.Write an equation for DeAndre's altitude, using x to represent the number of ladders DeAndre used (hint: a ladder takes DeAndre down in altitude, so the coefficient should be negative).
Set up a function A(x) for altitude, where x is the number of ladders used. Each ladder takes DeAndre down 10 feet, so this would be -10x. And DeAndre starts at 186 feet, so we'd have:
[B]A(x) = 186 - 10x[/B]

Find the explicit formula of the sequence 3,12,48

Find the explicit formula of the sequence 3,12,48
We [URL='https://www.mathcelebrity.com/sequenceag.php?num=3,12,48&n=10&pl=Calculate+Series']type in 3,12,48 into our search engine[/URL]. Choose series, and we get:
[B]a(n) = 3 * 4^(n - 1)[/B]

Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episod

Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episode airs, Jake receives a bunch of fan mail. He splits all the letters into 3 equal stacks to open with his mom and his sister. Each stack contains 21 letters. Which equation can you use to find the number of letters n Jake receives?
The number of letters n is represented by number of stacks (s) times letter per stack (l). We're given s = 3 and l = 21, so we have:
n = 21(3)
n = [B]63[/B]

MAPE - MPE - MAPD

Free MAPE - MPE - MAPD Calculator - Given a time series of actual and forecasted values, this determines the following:

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index

Free Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index Calculator - Given a series of cash flows C_{t} at times t and a discount rate of (i), the calculator will determine the Net Present Value (NPV) at time 0, also known as the discounted cash flow model.

Profitability Index

Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

Profitability Index

Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

Oakdale School is sponsoring a canned food drive. In the first week of the drive, the students colle

Oakdale School is sponsoring a canned food drive. In the first week of the drive, the students collected 638 cans. They collected 698 cans in the second week and 758 cans in the third week. If the students continue to collect cans at this rate, in which week will they collect more than 1,000 cans?
We have an arithmetic sequence where each successive term increases by 50.
[URL='https://www.mathcelebrity.com/sequenceag.php?num=638%2C698%2C758&n=10&pl=Calculate+Series&a1=5&d=3']Using our sequence calculator[/URL], we find that week #8 is when the students cross 1,000 cans.

The next number in the series 2,5,11,20,32,47, is

The next number in the series 2,5,11,20,32,47, is
[LIST]
[*]2 + 3 = 5
[*]5 + 6 = 11
[*]11 + 9 = 20
[*]20 + 12 = 32
[*]32 + 15 = 47
[/LIST]
Notice the addition pattern:
3, 6, 9, 12, 15
This means our next term is:
47 + (15 + 3)
47 + 18
[B]65
[MEDIA=youtube]mAj3tqXUbZs[/MEDIA][/B]

The next number in the series 38 36 30 28 22 is

The next number in the series 38 36 30 28 22 is
Notice the change of factors.
Subtract 2, Subtract 6, Subtract 2, Subtract 6.
So the next number should subtract 2.
22 - 2 = [B]20
[MEDIA=youtube]x7SHk_6-aok[/MEDIA][/B]

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that s

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that starts with 13 and continues to add seven to each output. For now, van needs to know what the 15th output will be. Complete the steps needed to determine the 15th term in sequence.
Given a first term a1 of 13 and a change amount of 7, expand the series
The explicit formula for an [I]arithmetic series[/I] is an = a1 + (n - 1)d
d represents the common difference between each term, an - an - 1
Looking at all the terms, we see the common difference is 7, and we have a1 = 13
Therefore, our explicit formula is an = 13 + 7(n - 1)
If n = 15, then we plug it into our explicit formula above:
an = 13 + 7(n - 1)
a(15) = 15 + 7(15 - 1)
a(15) = 15 + 7 * 14
a(15) = 15 + 98
a(15) = [B]113[/B]

What is the 1000th term in the series 0, 7, 14, 21, … ?

Map this out as a function with term number n and value
1, 0
2, 7
3, 14
4, 21
The values jump by 7, but they do so as the n - 1 term.
We have the series formula S(n) = 7(n - 1)
The problem asks for S(1000)
S(1000) = 7(1000 - 1)
S(1000) = 7(999)
S(1000) = [B]6,993[/B]
[MEDIA=youtube]ZF10Ec29XKo[/MEDIA]