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Masja [62]
2 years ago
12

How to use two terms to find a1,d, and an For the arithmetic sequence?

Mathematics
1 answer:
emmasim [6.3K]2 years ago
3 0

Answer:

  d = (a[n2] -a[n1])/(n2 -n1)

  a1 = a[n1] -d(n1 -1)

Step-by-step explanation:

The generic term is ...

  an = a1 +d(n -1)

Fill in the values associated with the two terms and solve the simultaneous equations.

For terms n1 and n2, their difference will be ...

  a[n2] -a[n1] = (a1 +d(n2 -1)) -(a1 +d(n1 -1)) = d(n2 -n1)

Dividing by the coefficient of d tells you ...

  d = (a[n2] -a[n1])/(n2 -n1)

Once you have the value of d, you can find the first term.

  a[n1] = a1 +d(n1 -1)

  a1 = a[n1] -d(n1 -1)

_____

<u>Example</u>:

  3rd term = 12

  7th term = 20

  d = (20 -12)/(7 -3) = 8/4 = 2

 a1 = a3 -d(3 -1) = 12 -2(2) = 8

The n-th term is ...

  an = a1 +d(n -1)

  an = 8 +2(n -1)

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What is the constant of proportionality in the equation y=12.9x?<br> Enter your answer as a decimal
forsale [732]

Answer:

The constant of proportionality would just be 12.9.

Step-by-step explanation:

This equation is already simplified enough to were the constant of proportionality is just the number attached to the x.

3 0
3 years ago
I need help figuring out X, i’ve been trying multiple solutions and I still don’t get what I have to do.
zhenek [66]

Answer: 5

Step-by-step explanation:

47+ 16x-4 +12x-3 =180

28x +40 =180

28x = 140

X= 5

5 0
2 years ago
How would you write y=2/3x+1/3 in point slope form??
gladu [14]

Answer:

y - 1 = 2/3(x - 1).

Step-by-step explanation:

Point slope form is y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.

y = 2/3x + 1/3   which gives the slope m = 2/3.

We can now find a point on the line by putting x = 1 say then find y:

y  = 2/3(1) + 1/3  =  2/3 + 1/3 = 1 so  the point is (1, 1).

(x1, y1) = (1, 1)

So the answer is ;

y - 1 = 2/3(x - 1).

6 0
3 years ago
If the areas of the given pairs of shapes are equal, find the value of x.​
den301095 [7]

Answer:

x = 8cm

Step-by-step explanation:

we are given a square and rectangle.we want to figure out x which is the width of the rectangle. we are also given a condition i.e

  • the area of the square equal to the area of the rectangle

therefore,

\displaystyle \rm A _{square } = A _{rect}

recall the formula of the area of square and rectangle so,

\displaystyle  {s}^{2} = lw

now assign variables

  • s \implies16cm
  • l \implies32cm
  • w \implies x

thus substitute:

\displaystyle 32cmx =  {16cm}^{2}

simplify square:

\displaystyle 32cmx = 256cm^2

divide both sides by 32:

\displaystyle  \boxed{x = 8cm}

and we're done!

3 0
2 years ago
Read 2 more answers
What is the value of n? n–2= 10n+ 4/2 Enter your answer in the box.
pentagon [3]

Answer:

-4 / 9

Step-by-step explanation:


 n - 2 = 10n + 4/2

 n - 10n = 4/2 + 2

 -9n = 4/2 + 4/2 ( taking LCM of 4/2 and 2)

 -9n = 8/2

 -9n = 4

    n = 4 / -9

   

   therefore n = -4 /9 ( since the minus sign doesn't make a difference whether placed at numerator or denominator) .


7 0
3 years ago
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