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
Varvara68 [4.7K]
3 years ago
5

Find the sum of the first 12 terms of the sequence. 1, -4, -9, -14, . . . (2 points)

Mathematics
2 answers:
egoroff_w [7]3 years ago
8 0

Answer:

sum of the first 12 terms of the sequence. 1, -4, -9, -14, . . = -318

Step-by-step explanation:

The given AP is,

1, -4, -9, -14, . . .

first term a = 1,

common difference d = -4 - 1 = -5

number of terms  n = 12

<u>Equation:</u>

Sum of n terms of AP, S₁₂ = n/2[2a + (n - 1)d]

S₁₂ = 12/2[(2*1) + (12 - 1)*(-5)]

S₁₂ = 6[2 + (11*(-5))]

S₁₂ = 6[2 - 55] = 6*(-53) = -318

Therefore sum of the first 12 terms of the sequence. 1, -4, -9, -14, . . = -318

omeli [17]3 years ago
5 0

Answer:

The sum of first 12 terms of the sequence. 1, -4, -9, -14, . .  is -318.

Step-by-step explanation:

Given sequence  1, -4, -9, -14, . . .

We have to find the sum of first 12 terms of the sequence. 1, -4, -9, -14, . .

Consider  the given sequence 1, -4, -9, -14, . . .

a_1=1 ,a_2=-4,a_3=-9

First calculate the common difference (d)

a_2-a_1=-4-1=-5\\a_3-a_2=-9+4=-5

Thus, common difference is -5

We know sum of terms in an Arithmetic progression is given by,

S_n=\frac{n}{2}(2a+(n-1)d)

where n is number of terms ,

a = first term

d = common difference

Here, n = 12 , a= 1 , d = -5

S_{12}=\frac{12}{2}(2(1)+(12-1)(-5))

Solving , we get,

S_{12}=6(2+11(-5))

S_{12}=6(2-55)

S_{12}=6(-53)

S_{12}=-318

Thus, the sum of first 12 terms of the sequence. 1, -4, -9, -14, . .  is -318.

You might be interested in
Which is the most economic way to lessen electric consumption?
AysviL [449]

Answer:

1) c. Use only appliances to do the most important task in the house.

2) b. 112kwh

3) b. 111kwh

Step-by-step explanation:

Energy can be defined as the ability (capacity) to do work and it's measured in Joules. The various forms of energy are solar energy, chemical energy, thermal energy, wind energy, nuclear energy, electrical energy, etc.

Power can be defined as the energy required to do work per unit time.

Mathematically, it is given by the formula;

Power = \frac {Energy}{time}

Energy consumption is the total amount of power used by an electronic device per unit time and it's measured in Watt-hour or Kilowatt-hour.

Mathematically, it is given by the formula;

Energy = power * time

Generally, the most economic way to lessen electric consumption is by ensuring only the important electrical appliances are used at all times.

2. Given the following data;

Previous reading = 2156 KWh

Present reading = 2268 KWh

To find how many kilowatt-hour was consumed;

Energy consumption = present reading - previous reading

Energy consumption = 2268 - 2156

<em>Energy consumption = 112 KWh</em>

3. Given the following data;

Previous reading = 5512 KWh

Present reading = 5623 KWh

To find the electrical consumption of Falogme Family;

Electrical consumption = present reading - previous reading

Electrical consumption = 5623 - 5512

<em>Electrical consumption = 111 KWh</em>

6 0
3 years ago
A cylinder with a height of 4 m has a volume of approximately
tigry1 [53]

Answer:

18m

Step-by-step explanation:

113.04m/3.14 = 36m/4m = 9m*2 = 18m

7 0
3 years ago
Write the first ten terms of the geometric sequence a1 = 3, r = 1.1 to two decimal places. Am I supposed to multiply 3 by 1.1 te
Makovka662 [10]
The general formula for geometric series is tn = a×rⁿ⁻¹. In this question, a (or a1) is 3, and r is 1.1, therefore the first ten terms would be 3×1.1⁰ (3) , 3×1.1¹ (3.3), 3×1.1² (3.63) and so on up until you get to 3×1.1⁹ or 7.07.
6 0
3 years ago
7x - 3x = 24
Debora [2.8K]
7x - 3x = 24
The 7x and the 3x are both like terms, so they can be combined. 7 - 3 is 4, so the equation turns into
4x = 24
Now, you want to get the x alone, so you divide both sides by 4 because it is the opposite of multiplication. 24 divided by 4 is 6, so
x = 6
4 0
3 years ago
Read 2 more answers
When no more than 110 units are produced, the cost of producing y units is given by C(x).
Maslowich

Producing 73.8 units gives the lowest possible average cost.

The average cost (AC) is the ratio of the total cost to the number of units produced. It is given by:

AC = C(x) / x

AC = (0.2x³ – 24x² + 1514x +30064) / x

AC = 0.2x² - 24x + 1514 + 30064/x

The lowest possible average cost is at AC' = 0. Hence differentiating the average cost, gives:

AC' = 0.4x - 24 - 30064/x²

0.4x - 24 - 30064/x² = 0

0.4x³ - 24x² - 30064 = 0

Solving the cubic polynomial gives:

x = 73.8 units

Therefore the lowest possible average cost is when 73.8 units are produced.

Find out more at: brainly.com/question/20346871

6 0
3 years ago
Other questions:
  • The amphitheater has two types of tickets available, reserved seats and lawn seats. The maximum capacity of the venue is 20,000
    11·1 answer
  • CAN SOMEONE HELP ME ASAP THANK YOU SO MUCH :{
    10·1 answer
  • What are the quotient and remainder of (3x^3-2x^2-8)/(x+5)
    12·2 answers
  • What is the answer to the problem 1/2x=14
    5·2 answers
  • Which expression is equivalent to 1 - 2 over 3 to the -3rd power
    9·1 answer
  • How do you change 0.35 to a whole. number
    5·1 answer
  • I need help with both boxes plz help thanks
    8·1 answer
  • ASAP please it’s very important
    9·1 answer
  • Need help with number 11 ASAP!!!!
    12·2 answers
  • Halp me halp me halp me halp me plss
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!