MATHEMATICS HIGH SCHOOL

4. Find the sum of the first eighteen terms of the arithmetic sequence whose nthterm is an = 15 + 8n.
a. 1438
b. 1638
c. 1836
d. 1783​

Answers

Answer 1
Answer:

Answer:

The sum of first eighteen terms of the arithmetic sequence is \mathbf{S_(18)=1638}

Option B is correct option.

Step-by-step explanation:

We need to find the sum of the first eighteen terms of the arithmetic sequence whose nth  term is an = 15 + 8n

The formula used to calculate sum of arithmetic sequence is: S_n=(n)/(2)(a_1+a_n)

Finding a₁ by putting n=1

a_n=15+8n\na_(1)=15+8(1)\na_(1)=15+8\na_(1)=23

We have a_1=23

Finding 18th term n=18

a_n=15+8n\na_(18)=15+8(18)\na_(18)=15+144\na_(18)=159

So, the sum of first eighteen terms of the arithmetic sequence is:

S_n=(n)/(2)(a_1+a_n)\nS_(18)=(n)/(2)(a_1+a_(18))\nS_(18)=(18)/(2)( 23+159)\nS_(18)=9(182)\nS_(18)=1638

So, the sum of first eighteen terms of the arithmetic sequence is \mathbf{S_(18)=1638}

Option B is correct option.

Related Questions

a Potter uses three fifths of a pound of clay to make a bowl how many bowls could the potter make from 10 pounds of clay
A bag contains 9 red chips and 12 blue chips. Two chips are selected randomly without replacement from the bag. What is the probability that the two chips are the same color?That would be the probability of two reds PLUS the probability of two blues.The probability of two reds is (9/21)*(8/20) = 72/420 The probability of two blues is (12/21)*(11/20) = 132/420. The sum is 204/420 = 51/105 = 45.87% A magician asks you to pick a card, any card from a standard deck of 52 cards. What is the probability of picking an ace?A magician asks you to pick a card, any card from a standard deck of 52 cards. What is the probability of picking an ace?lucy fills a pot with a mixture of 1200 black beans and 300 white beans, all the same size. When she grabs a handful of 15 beans, she finds that 10 are black. What is the probability of choosing a white bean?
Write 9/12 as a decimal
which has more volume a cube of sides measuring 4 units each or a sphere with a radius of 3 units
What are the next three terms in the sequence? -1,9,19,29,.... A=38,37,32 B=40,51,62 C=39,49,59 D=38,47,56

Harry's rectangular side yard is 2 yards by 14 yards with an area of 28 square yards. Which dimensions have the same area

Answers

4 yards by 7 yards. 2 multiplied by 14 is 28, and 4 multiplied by 7 is also 28.

On her first three 5-point math quizzes, Ami’s scores were 4,3, and 5. She will take 3 more quizzes this semester. What three scores would give her an average that is a whole number? A repeating decimal?

Answers

On her first three 5-point math quizzes, Ami’s scores were 4,3, and 5. She will take 3 more quizzes this semester. What three scores would give her an average that is a whole number? A repeating decimal?

Answer: The three scores 2, 5, and  5 would give her an average that is a whole number.

Average = (4+3+5+2+5+5)/(6) =(24)/(6) =4

The three scores 5, 5, and 3 would  give her an average that is a repeating decimal

Average = (4+3+5+5+5+3)/(6) =(25)/(6) =4.166667

Please help I've been stuck on this question for a while now. How do I solve (1/2)^4 (1/2)^-2? It has to do with Multiplying and Dividing Expressions with Exponents. Please show work so I may figure it out on my own.

Answers

The value of the expression is 0.25

Explanation:

The expression is $\left((1)/(2)\right)^(4)\left((1)/(2)\right)^(-2)$

Since, the base of the expression is the same. Then, by "product rule", when multiplying two powers that have the same base, you can add the exponents.

Thus, we have,

$\left((1)/(2)\right)^(4)\left((1)/(2)\right)^(-2)=\left((1)/(2)\right)^(4-2)$

Adding the exponents, we have,

$\left((1)/(2)\right)^(4)\left((1)/(2)\right)^(-2)=\left((1)/(2)\right)^(2)$

Applying exponent rule, $\left((a)/(b)\right)^(c)=(a^(c))/(b^(c))$, we have,

$\left((1)/(2)\right)^(2)=(1^(2))/(2^(2))$

Simplifying, we get,

(1)/(4)

Dividing, we have,

0.25

Thus, the value of the expression is 0.25

9 students volunteer for a committee. How many different 6-person committees can be chosen?a. 1 b. 362,880 c. 60,480 d. 84

Answers

9\cdot8\cdot7\cdot6\cdot5\cdot4=60,480\n\nAnswer:D

Alex and his friends are studying for a geometry test and one of the main topics covered is parallel lines in a plane. They each write down what they think it means for two distinct lines in a plane to be parallel:Rachel writes, ''two distinct lines are parallel when they are both perpendicular to a third line.''



Alex writes, ''two distinct lines are parallel when they do not meet.''



Briana writes, ''two distinct lines are parallel when they have the same slope.''

Analyze each definition, indicating if it is mathematically correct and if it has any drawbacks.

helpp pleaseee

Answers

Briana is correct because she is smart

Step-by-step explanation:

Briana is correct because she is smart

During which stage of engine operation does the burning mixture of air and fuel force the piston downward? A. Compression
B. Ignition
C. Power
D. Exhaust

Answers

the answer would be B
Other Questions
How to solve -5/7-11/7x=-y 2y=7+5x
Which fraction can be represented with a repeating decimal?3/2012/57/164/11
A football is kicked toward the goal. The height of the ball is modeled by the function h(x) = -16t^2 + 64t where t equals the time in seconds and h(x) represents the height of the ball at time t seconds. What is the axis of symmetry and what does it represent?A. x = 2; it takes 2 seconds to reach the maximum height and 2 seconds to fall back to the ground B. x = 2; it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground C. x = 4; it takes 4 seconds to reach the maximum height and 4 seconds to fall back to the ground D. x = 4; it takes 4 seconds to reach the maximum height and 8 seconds to fall back to the ground
the volumes of two spheres are 729 in3 and 27 in3. what is the ratio of their radii, rounded to the nearest whole number?