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
riadik2000 [5.3K]
3 years ago
15

In an arithmetic series, the sum of the first 12 terms is equal to ten times the sum of the first 3 terms. If the first term is

5, find the common difference and the value of S20.
Mathematics
1 answer:
arlik [135]3 years ago
8 0

Answer:

Step-by-step explanation:

The formula for determining the sum of the first n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

If a = 5, the expression for the sum of the first 12 terms is

S12 = 12/2[2 × 5 + (12 - 1)d]

S12 = 6[10 + 11d]

S12 = 60 + 66d

Also, the expression for the sum of the first 3 terms is

S3 = 3/2[2 × 5 + (3 - 1)d]

S3 = 1.5[10 + 2d]

S3 = 15 + 3d

The sum of the first 12 terms is equal to ten times the sum of the first 3 terms. Therefore,

60 + 66d = 10(15 + 3d)

60 + 66d = 150 + 30d

66d + 30d = 150 - 60

36d = 90

d = 90/36

d = 2.5

For S20,

S20 = 20/2[2 × 5 + (20 - 1)2.5]

S20 = 10[10 + 47.5)

S20 = 10 × 57.5 = 575

You might be interested in
Find an equation for the line with the given properties. Express the equation in slope-intercept form.
EleoNora [17]

Answer:

y = 3x - 19

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Define variables

Slope <em>m</em> = 3

Random point (5, -4)

Step 2: Plug in known variables

y = 3x + b

Step 3: Find <em>b</em>

-4 = 3(5) + b

-4 = 15 + b

b = -19

Step 4: Write linear equation

y = 3x - 19

8 0
3 years ago
A rectangular prism has a length of 1514 centimeters, a width of 8 centimeters, and a height of 214 centimeters. Enter the volum
vichka [17]
Hewwo dere fello citizen, The answer is 274 1/2cm! Rate me five stars and meow! :3
7 0
3 years ago
Read 2 more answers
A triangular pyramid has these dimensions.
marishachu [46]

Answer: 42 cm3

Step-by-step explanation:

7 0
3 years ago
If B is the midpoint of AC, AC= CD, AB=3x+4, AC= 11x-17, and CE= 49 , find DE
melisa1 [442]

Answer:

Ehhh

Step-by-step explanation:

4 0
2 years ago
The expression 0.09x+(x-30) models the final price of a bicycle is its an instant rebate in a state that charges a sales tax. Th
svlad2 [7]

Answer:

<em>A)0.09x</em>

Step-by-step explanation:

The original price of the bicycle is x.

The discounted price of the bicycle is x - 30. It is a $30 discount.

The tax goes on the original price. 0.09x is the 9% tax applied to the original price x.

Answer: 0.09x

6 0
2 years ago
Read 2 more answers
Other questions:
  • What number is 40% of 30? Will Upvote
    14·1 answer
  • Whats an strategy you could use to compare 2 out of 6 and 5 out of 8
    8·1 answer
  • Find the median of the following set of data. Round to the nearest tenth if necessary. 26.1, 8.4, 11.4, 44.1, 32.3, 46, 41, 18.5
    11·2 answers
  • 3 ( x - 4 ) = 2x = 6
    7·2 answers
  • What is the domain of the function shown in the mapping?
    8·1 answer
  • What is the percent of the cars were going above 80 mph!
    7·2 answers
  • Is this correct? (Geometry hw)
    5·2 answers
  • What is the mode of the following numbers 5,4, 10, 3, 3, 4, 7, 4, 6, 5, 11, 9, 5, 7
    9·2 answers
  • I need the csc for this same problem
    14·2 answers
  • Use elimination to solve each<br> system of equations<br> 3x + 5y = -2<br> 3x - 2y = - 16
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!