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
lara31 [8.8K]
3 years ago
13

If 2k, 5k-1 and 6k+2 are the first 3 terms of an arithmetic sequence, find k and the 8th term​

Mathematics
1 answer:
Klio2033 [76]3 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = a_{2} - a_{1} = a_{3} - a_{2}

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

--------------------------------------------------------

The n th term of an arithmetic sequence is

a_{n} = a_{1} + (n - 1)d

a_{1} = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

a_{8} = 4 + (7 × 5) = 4 + 35 = 39

You might be interested in
1/5 divided by 4 equals to what
Dima020 [189]

Answer:

1/5 divided by 4 equals to 0.05

7 0
2 years ago
Please factorise 16p²-9q² for me<br>​
kirill115 [55]

Answer:

a ^ 2 - b ^ 2 = ( a + b ) ( a - b ) where a = 4p and b = 3q.

( 4p + 3q ) ( 4p - 3q )

7 0
3 years ago
Mrs. Sanchez is given a $550 hiring bonus with a new job. She earns an average commission of $275 per week for the year. If $68
Goshia [24]
She would get $11,314 for the year.
8 0
3 years ago
Read 2 more answers
What is the solution for the equation StartFraction 5 Over 3 b cubed minus 2 b squared minus 5 EndFraction = StartFraction 2 Ove
wolverine [178]

Answer:

The solutions are:

b=0,\:b=4

Step-by-step explanation:

Considering the expression

  • \frac{5}{3b^3-2b^2-5}=\frac{2}{b^3-2}

Solving the expression

\frac{5}{3b^3-2b^2-5}=\frac{2}{b^3-2}

\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c

5\left(b^3-2\right)=\left(3b^3-2b^2-5\right)\cdot \:2

5b^3-10=6b^3-4b^2-10

\mathrm{Switch\:sides}

6b^3-4b^2-10=5b^3-10

6b^3-4b^2-10+10=5b^3-10+10

6b^3-4b^2=5b^3

\mathrm{Subtract\:}5b^3\mathrm{\:from\:both\:sides}

6b^3-4b^2-5b^3=5b^3-5b^3

b^3-4b^2=0

Using\:the\:Zero\:Factor\:Principle: if\:\mathrm ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)

So,

b=0,b-4=0

b=0,b=4

Therefore, the solutions are:

b=0,\:b=4

4 0
3 years ago
Read 2 more answers
How to simplify the expressions of 5p-5-10-2p
Arada [10]

Answer:

3p - 15

Step-by-step explanation:

5p - 2p = 3p

-5 - 10 = -15

3p + - 15 = 3p - 15

4 0
3 years ago
Other questions:
  • 50 POINTS HELP HELP PLZ
    15·2 answers
  • Translate algebraic expression. <br><br>1) One-fourth of the sum of 6 and s?
    9·1 answer
  • Find the values of p and q such that 4x^2+12x=4(x+p)^2-q
    8·1 answer
  • if the zeroes of the polynomial, p(x)= ax^3 + 3bx^2 + 3cx + d = 0 be alpha - beta, alpha and alpha + beta. Prove that 3abc = a^2
    15·1 answer
  • LAST TIME I PUT THIS UP OFFERING A LOT OF POINTS SOME ONE PLEASE!!!!
    5·1 answer
  • Look at The Screenshot
    8·2 answers
  • Please I need some answers
    10·1 answer
  • Explain why the equation is not linear 2x^2+y=7
    9·1 answer
  • Is (12 + 12)7 × 37 equivalent to (24 × 3)7?
    9·1 answer
  • Find the slope of the line.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!