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
ivanzaharov [21]
4 years ago
6

The first term of an arithmetic sequence is −12 . The common difference of the sequence is 7. What is the sum of the first 30 te

rms of the sequence? Enter your answer in the box.
Mathematics
1 answer:
Olenka [21]4 years ago
8 0

Answer:

2685

Step-by-step explanation:

The nth term of an arithmetic sequence is:

aₙ = a₁ + d (n − 1)

where a₁ is the first term and d is the common difference.

Here, a₁ = -12 and d = 7:

aₙ = -12 + 7 (n − 1)

aₙ = -12 + 7n − 7

aₙ = -19 + 7n

The sum of the first n terms of an arithmetic sequence is:

S = (n/2) (a₁ + aₙ)

First, we find the 30th term:

a₃₀ = -19 + 7(30)

a₃₀ = 191

Now we find the sum:

S = (30/2) (-12 + 191)

S = 2685

You might be interested in
what is 10 x 10 x 10 divided by 9? ik but my comments r maxed out for this one place and yall get points
topjm [15]

Answer:

10 x 10 x 10 divided by 9? =111.111111111

3 0
3 years ago
Read 2 more answers
|x^2+x-1|=1 solve for x
Marizza181 [45]

<span><span>x=<span>−3</span></span><span>x=<span>-3</span></span></span>

Here the steps

<span><span><span>2<span>x+1</span></span>−<span>1<span>x−1</span></span>=<span><span>2x</span><span><span>x2</span>−1</span></span></span><span><span>2<span>x+1</span></span>-<span>1<span>x-1</span></span>=<span><span>2x</span><span><span>x2</span>-1</span></span></span></span>

 <span>x<span>−3</span></span><span><span>(<span>x+1</span>)</span><span>(<span>x<span>−1</span></span>)</span></span>=<span><span>2x</span><span><span>(<span>x+1</span>)</span><span>(<span>x<span>−1</span></span>)</span></span></span><span><span><span>x<span>-3</span></span><span><span>x+1</span><span>x<span>-1</span></span></span></span>=<span><span>2x</span><span><span>x+1</span><span>x<span>-1</span></span></span></span></span>

<span><span><span>(<span>x+1</span>)</span><span>(<span>x<span>−1</span></span>)</span></span><span><span>x+1</span><span>x<span>-1</span></span></span></span>

<span><span><span>x<span>−3</span></span>=<span>2x</span></span><span><span>x<span>-3</span></span>=<span>2x</span></span></span>

<span><span>x=<span>−3</span></span><span>x=<span>-<span>3</span></span></span></span>

<span><span><span><span>So the answer comes out to be x = 3 I hope this was helpful </span></span></span></span>

3 0
4 years ago
Y is directly proportional to x when y=30, x=6
rosijanka [135]

Answer:

a) y = 5x

b) y = 60

Step-by-step explanation:

Since, y is directly proportional to x when y=30, x=6

\therefore \:  y \:  \alpha \:  \: x \\ \therefore \:  y =  kx ...(1) \\ plug \: y = 30 \: and \: x = 6  \: in \: eq \: (1)\\ 30 = k \times 6 \\ k =  \frac{30}{6}  \\ k = 5 \\ plug \: k = 5 \: in \: (1) \\ y = 5x....(2) \: (required \: equation) \\ plug \: x = 12 \: in \: eq \: (2) \\ y = 5 \times 12 \\  \huge \red{ \boxed{y = 60}}

4 0
3 years ago
The model is made of stacks of plywood
sukhopar [10]

Answer:

what is the question your asking?

4 0
4 years ago
Read 2 more answers
Jamal and Samuel are saving for a camping trip. Jamal starts with $18 and saves $5 each week. Samuel starts with $10 and saves $
Liula [17]

Answer:

4 weeks

$28

Step-by-step explanation:

Let

x = number of weeks

Jamal's savings = 18 + 5x

Samuel's savings = 10 + 7x

Equate both savings

Jamal's savings = Samuel's savings

18 + 5x = 10 + 7x

18 - 10 = 7x - 5x

8 = 2x

x = 8 / 2

= 4

x = 4 weeks

Check:

18 + 5x

18 + 5(2)

18 + 10

= $28

Each boy would have saved an equal amount of $28 at the end of the 4th week

4 0
3 years ago
Other questions:
  • Ishaan is 727272 years old and William is 444 years old. How many years will it take until Ishaan is only 555 times as old as Wi
    6·1 answer
  • Ann is baking cookies.she bakes three dozen oatmeal raisin cookies,and four dozen chocolate chip cookies. Ann give away two doze
    14·1 answer
  • a trip from New York city to Seattle is 2,852.1 miles.  a family wants to make the drive in 10 days, driving the same number of
    9·2 answers
  • Please helppppppppppp
    12·1 answer
  • Find two positive real numbers whose product is a maximum. the sum is 80
    15·2 answers
  • suppose f(x)=33.3+1.4 log (x+1) models salinity of ocean water to depths of 1000 meters at a certain latitude. x is the depth in
    5·1 answer
  • If you vertically stretch the exponential function f(x) = 2^x by a factor of 5, what is the equation of the new function?
    15·1 answer
  • Find each difference. <br><br> (−5)−6=<br> 35−(−8)=<br> 5/2- 5/3 =<br> −4 8/3−(−1 4/1 )=
    9·1 answer
  • (need help ASAP) What is the probability of choosing a red jack or black king if you draw one card from a regular deck of 52 car
    14·1 answer
  • What is the missing angle in a triangle with angle measures of 15 degrees and 70 degrees
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!