You have to find the common difference, the term named in the problem, and the explicit formula.
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Question 1
Given the sequence
31, 61, 91, 121,...
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
computing the differences of all the adjacent terms
61 - 31 = 30, 91 - 61 = 30, 121 - 91 = 30
The difference between all the adjacent terms is the same and equal to
d = 30
As the first term of the sequence is:
a₁ = 31
now substituting a₁ = 31 and d = 30 in the nth term of the sequence
[tex]a_n=a_1+\left(n-1\right)d[/tex]
[tex]a_n=30\left(n-1\right)+31[/tex]
[tex]a_n=30n+1[/tex]
Now, putting n = 36 to determine the 36th term
[tex]a_n=30n+1[/tex]
[tex]a_{36}=30\left(36\right)+1[/tex]
[tex]a_{36}=1080+1[/tex]
[tex]a_{36}=1081[/tex]
Thus, the 36th term is:
[tex]a_{36}=1081[/tex]
Question 2
Given the sequence
-34, -44, -54, -64, ...
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
computing the differences of all the adjacent terms
[tex]-44-\left(-34\right)=-10,\:\quad \:-54-\left(-44\right)=-10,\:\quad \:-64-\left(-54\right)=-10[/tex]
The difference between all the adjacent terms is the same and equal to
[tex]d=-10[/tex]
As the first term of the sequence is:
a₁ = -34
now substituting a₁ = -34 and d = -10 in the nth term of the sequence
[tex]a_n=a_1+\left(n-1\right)d[/tex]
[tex]a_n=-10\left(n-1\right)-34[/tex]
[tex]a_n=-10n-24[/tex]
Now, putting n = 26 to determine the 36th term
[tex]a_n=-10n-24[/tex]
[tex]a_{26}=-10\left(26\right)-24[/tex]
[tex]a_{26}=-260-24[/tex]
[tex]a_{26}=-284[/tex]
Thus, the 26th term is:
[tex]a_{26}=-284[/tex]
Related Questions
Which describes this transformation?
Answers
need help finding x
Answers
Answer:
x=-8Step-by-step explanation:
[tex] \frac{6}{x - 1} = \frac{4}{x + 2} [/tex]
[tex]6x + 12 = 4x - 4[/tex]
[tex]6x - 4x = - 12 - 4[/tex]
[tex]2x = - 16[/tex]
[tex]x = - 8[/tex]
Please help me with the correct answer
Answers
Answer:
y=2(-2)+3
y=-1
y=2(-1)+3
y=1
y=2(0)+3
y=3
y=5
y=7
Answer:
(From left to right)
1st y (output): -1
2nd y (output): 1
3rd y (output): 3
4th y (output): 5
5th y (output): 7
Step-by-step explanation:
Substitute each x (input) into the given equation and solve. For example, to get the first y (output), substitute "-2" into the "x" in the equation, giving you "y = 2(-2) +3", then solve it.
Multiply 2(-2) to get -4, then add 3 to get -1.
Two angles are supplementary. The measure of one angle is 10 less than twice the measure of the other angle. Find the measures of the angles.
Answers
Step-by-step explanation:
Supplementry means which add up to 180°
Now, let's take one of them as x
And the other as x - 10
Now let's add : x + (x - 10) = 180°
2x - 10 = 180°
2x = 180 + 10
2x = 190
x = 190/2
x = 95
X = 95
x - 10 = 95 - 10
So, = 85
The 2 numbers are 95, and 85
Lets check!
95 + 85 = 180!
So therefore they are supplementry so it's right!
what is the percent of decrease from 2,000 to 60?
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Answer:
The answer is 97% decrease
how do I find the area (square inches)
Answers
Answer:
first one 49 2nd ones 25
Step-by-step explanation:
Which point on the number line best represents 10?
Help me plz
Answers
Answer: F
Step-by-step explanation:
Answer:
H
Step-by-step explanation:
3.3 x 3 = 9.9 which is close to 10 so its H
Need help. Offering brainliest and 20 points for this.
Answers
Answer:
[tex]4P+2G=96\\3P+1G=60 or 3P+G=60[/tex]
Step-by-step explanation:
Given in the question:
a) A family paid $96 for 4 pool passes and 2 gym memberships.
b) Later that day, an individual bought pool passes for herself and 2 of her friends, and 1 gym membership for her. She paid $60.
Let's write the system of equations for each purchase that happened in the scenario.
Let,
P=Price of each pool passes
G= Price of each gym membership
We get,
a) A family paid $96 for 4 pool passes and 2 gym memberships:
[tex]4P+2G=96[/tex]
b) Later that day, an individual bought pool passes for herself and 2 of her friends , and 1 gym membership for her. She paid $60:
[tex]3P+1G=60[/tex]
Therefore, the equations generated in the scenario were:
[tex]4P+2G=96\\3P+1G=60 or 3P+G=60[/tex]
Where,
P=Price of each pool passes
G= Price of each gym membership
PLEASE MARK ME AS BRAINLIEST
x + 23 = −4 need help
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Answer:
-27
Step-by-step explanation:
x+23−23=−4−23
x=−27
Help please I need this asap :’)
Answers
Answer: Line C
Step-by-step explanation:
Because when you use the slope formula on it you get a negative slope. Also the line in going down unlike the other lines which are goign up.
(x + 3)2 – (2x – 1)2
Answers
Answer:
-2x+8
Step-by-step explanation:
Help plz and please tell me how u got the answer
Answers
Answer:
I think is 2/3
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
COP is slope which is rise over run.
DOES ANYONE KNOW THE ANSWERS PLEASEEE (ILL GIVE BRAINLIST)!!!!
Answers
Is the following sequence arithmetic?
-14, 86, 186, 286, ...
A.No
B.Yes
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Simplify The ANSWER PLZ HELP ASAP DUE TOMORROW!
(9x+7)+(3m-2)+(8n+9)
Answers
Answer:
9x + 3m + 8n + 14
Step-by-step explanation:
Add all like terms.
7 -2 + 9 = 14
You can't do anything with the variables since they're all different.
9x + 3m + 8n + 14
Answer:
3m+8n+9x+14
Step-by-step explanation:
btw try math-way!! helps
12-(3r+2) = -7(r+6) show work please!!!!!
Answers
Answer:
-10r-32
Step-by-step explanation:
12-(3r+2)+-7(r+6)
12-3r-2-7(r+6)
12-3r-2-7r-42
-32-3r-7r
-32-10r
-10r-32
help me solve this please
A: ∠D≅∠N
B: NQ=5,PQ=12
C: ∠P≅∠N
D: No more information is needed; we already know they are similar.
Answers
Answer:
angle P congruent to angle N
Step-by-step explanation:
You know the angles at Q are congruent.
If angle P is congruent to angle N, then angle R is congruent to angle D.
Then both triangles are similar.
Please answer this question
Answers
Answer:
I think the scale factor would be 1/6
Answer:
1/6
Step-by-step explanation:
3 feet = 3*12 = 36
Scale factor = 6/36 = 1/6
Pls help only answer if you know the answer for sure.
Answers
Answer:
C
Step-by-step explanation:
If you graph this, it will be a straight line.
It is, therefore, a linear function.
I need help with this Geometry question. I think it’s law of sines :(
Answers
Answer:
17.628 = 17.6
Step-by-step explanation:
Someone cut a whole pizza into 3 equal parts she gave her four children the same amount of one of the sections what part of the whole pizza did she give each one of her children?
Answers
Answer: 1/12 of the whole pizza
Step-by-step explanation:
Someone cut a whole pizza into 3 pieces.
This means that the pizza was cut into 1/3 slices each.
She then gave her 4 children one of these sections to share equally.
The part each child got is:
= 1/3 ÷ 4
= 1/3 * 1/4
= 1/12 of the whole pizza
Note: When dividing fractions, you can multiply the first fraction by the inverse of the second fraction to find your answer.
help me please
A triangle has two sides of length 4 and 7. What is the smallest possible whole-number length for the third side?
Answers
Answer:
The smallest possible length for the 3rd side must be 4
Step-by-step explanation:
Any 2 sides combined must be greater than the 3rd side
Jackson is building a sandbox for his son. He needs to fill it with about 1 1 /2 feet of sand. If his sandbox is 4 feet by 2 feet and sand comes in bags that fill two cubic feet of space, how many bags will Jackson have to buy in order to fill his son’s sandbox?
Answers
Answer:
6 Bags
Step-by-step explanation:
Volume: LxWxH
L=4
W=2
H=1 1/2
8x 1/12= 12
12/2 = 6
Ans: 6 Bags
3y + 5x =15
dhnsnsishbsdn
Answers
Answer:
x= −3/5y +3 y= -5/3 + 5
Step-by-step explanation:
Answer:
If we are solving for y we move all terms that don't contain y to the right side and solve.
So y = 5 - 5x/3
what is an equation of a line that has a slope of 6 and a y-intercept of (0,12)
Answers
Simplify:
-5(6x + 3y - 1)
A. - 30x - 15y- 5
B. -30x - 15y +5
OC. – 30x + 15y - 5
D. --30x + 15y + 5
NEED HELP
Answers
If f(x)=x-6 and g(x)=x^1/2(x+3) , find g(x) X f(x) .
Answers
Answer:
(B).
Step-by-step explanation:
√x(x + 3)(x - 6) = √x(x² - 3x - 18) = [tex]\sqrt{x^{5} }[/tex] - 3[tex]\sqrt{x^{3} }[/tex] - 18√x
ella purchased 9 rews & umpts for about $24. Rews are $1 each and umpts are $6. write a system of equations in standard form to model relationship between rews (x) and umpts (y)
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Gerardo divides 1/2 by 2, and then divides the quotient by 2 again. Draw a circle to represent one whole. Then use it to explain how Gerardo's work is similar to dividing 1/2 by 4.
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Answer:
Kindly check attached picture for circle illustration.
Step-by-step explanation:
The whole circle = 1
Half the circle = semicircle = 1/2
Half the semicircle = 1/4
Half of 1/4 = 1/8
Hence, Geraldo would obtain 1/8
Normal calculation:
1/2 ÷ 2
1/2 * 2/1 = 1/4
Quotient = 1/4
Quotient / 2
1/4 ÷ 2
1/4 * 1/2
= 1/ 8
Find the value of 42 - (-10)
*explain how to solve*
Answers
Answer: 52
Step-by-step explanation:
42-(-10) first since your multiplying the two negative signs with each other it turns into a positive and looks like 42+10 and 42+10=52
