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
german
3 years ago
7

"Find the sum of the first 50 term in this sequence 4, 7, 10, 13, ...". How do i do this without writing them all out, and how d

o i develop a formula?
Mathematics
1 answer:
melisa1 [442]3 years ago
5 0
First term ,a=4 , common difference =4-7=-3, n =50
sum of first 50terms= (50/2)[2×4+(50-1)(-3)]
=25×[8+49]×-3
=25×57×-3
=25× -171
= -42925
derivation of the formula for the sum of n terms
Progression, S
S=a1+a2+a3+a4+...+an

S=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d]   →   Equation (1)

S=an+an−1+an−2+an−3+...+a1

S=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n−1)d]   →   Equation (2)

Add Equations (1) and (2)
2S=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an)

2S=n(a1+an)
S=n/2(a1+an)

Substitute an = a1 + (n - 1)d to the above equation, we have
S=n/2{a1+[a1+(n−1)d]}
S=n/2[2a1+(n−1)d]
You might be interested in
Which point lies on the line with point slope equation y-3=4(x+7)
IRISSAK [1]

Answer:

-7,3

Step-by-step explanation:

4 0
3 years ago
Is this a quadratic function 2x+13=13
lys-0071 [83]

Answer:

Step-by-step explanation:

Simplifying

2x + 13 = 0

Reorder the terms:

13 + 2x = 0

Solving

13 + 2x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-13' to each side of the equation.

13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0

0 + 2x = 0 + -13

2x = 0 + -13

Combine like terms: 0 + -13 = -13

2x = -13

Divide each side by '2'.

x = -6.5

Simplifying

x = -6.5

7 0
1 year ago
H2 + 7h + 10 = 0<br> Help please
Leni [432]

Answer:

-2, -5

Step-by-step explanation:

h2 + 7h + 10 = 0

h^2 +7h + 10 = 0

h^2 +2h +5h + 10 = 0

h(h+2) + 5(h+2) = 0

h+2 = 0 or h+5 = 0

h = -2 or h = -5

4 0
3 years ago
Help me please thanks
mars1129 [50]

Answer:

x  <  − 5

The notation would be ( − ∞ ,  − 5 )

On the graph, you would put an open dot on -5 and an arrow continuing down it

7 0
3 years ago
Read 2 more answers
Better to be a free bird than a captive king
Cerrena [4.2K]
What is the question?
5 0
3 years ago
Other questions:
  • Use rounding numbers to estimate the sum of 171 + 727
    10·2 answers
  • (15points) Please help me with this bonus!! I really need help!!
    13·2 answers
  • when walking home from school during the summer months, Harold buys either an ice-cream or a drink from the corner shop. If Haro
    15·1 answer
  • Lashonda wants to buy a new boat but needs money for the down payment. Her parents agree to lend her money at an annual rate of
    7·1 answer
  • Complete the function for this graph.
    6·1 answer
  • Help please. it would really help if someone explained
    12·1 answer
  • What do I do her just tell me​
    6·1 answer
  • Given that a company's basic work week is 40 hours. If an employee works 48 hours for the week. How many hours of overtime did t
    6·1 answer
  • 2 2/10 - 16 2/11 i need answer pls
    11·2 answers
  • A board is 105 inches long how long is it in feet and inches
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!