1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vanyuwa [196]
3 years ago
13

18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
8 0

a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}

S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525

You might be interested in
Given a circle with measures of (C, d, and r) and a circle with measures of (C', d', and r'), what is C if d d' = 0.25 and C' =
sattari [20]

Mathematically, C’ = πd’

C’ =16, π = 22/7

∴ 16 = 22d’/7

16 x 7 = 22d’

d' = (16 x 7) / 22

<span>d’ = 112/22</span>

d’ = 5.09

 

d d’ = 0.25

d’ = 5.09

∴ d (5.09) = 0.25

d = 0.25/5.09

d = 0.05

 

Mathematically, C = πd

π = 22/7, d = 0.05

∴ C = 22/7 x 0.05

<span>C = 0.16</span>

7 0
3 years ago
Read 2 more answers
Solve for the variable
liraira [26]

Answer:

y = 25

Step-by-step explanation:

30=\frac{6}{5} y\\\\\frac{6}{5} y=30\\\\(\frac{6}{5} y)5=30*5\\\\6y=150\\\\\frac{6y=150}{6}\\\\\boxed{y=25}

Hope this helps!

8 0
3 years ago
A particle shade of orange paint has 2 cups of yellow paint for every 3 cups of red paint on the double number line circle the v
Marat540 [252]

Answer:

Given,

2 cups of yellow paint is needed for every 3 cups of red paint to make a batch of orange paint,

So, the ratio of yellow paint and red paint in a batch of orange paint = 2 : 3

Make two number lines,

First one represents the multiple of 2 and second one represents the multiples of 3,

By the double number line ( shown below ),

It is clear that,

For 3 batches of orange paint, 6 cups of yellow paint and 9 cups of red paint are needed.

7 0
3 years ago
Why is x=5 not in the domain of the function
Anestetic [448]
BC it's a rate of change
5 0
2 years ago
7.4: How do You Know?
lianna [129]

Answer:

The one on the right is 25 percent smaller then the one on the left. They have he same angle measures.  The line lengths are just different.

Step-by-step explanation:

Hope this helps.

3 0
2 years ago
Other questions:
  • The area of circle Z is 64x ft?.
    6·1 answer
  • The question is in the picture.
    11·1 answer
  • How do you factor this?<br> 2z^2-12z+10=0
    13·2 answers
  • Evaluate –x + (–5.8) for x = 7.1.<br><br> –1.3<br> 12.9<br> –12.9<br> 1.3
    15·2 answers
  • Mrs. Summer's third grade class is putting on a play. If she has 13 1/8 yards of fabric, and each student needs 7/8 of a yard fo
    14·2 answers
  • Find last year's salary if after a 6% pay raise this year's salary is $36,040
    9·1 answer
  • The length of an edge of a cube is 5 in. what is the volume of the cube?
    15·1 answer
  • Please help me with this ^
    15·1 answer
  • -12÷3×(-8 +(-4)^2 -6)+2<br><br>Please explain in detail.
    9·2 answers
  • Sam used algebra tiles to make this model of an equation. Based on Sam's equation what statement is true.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!