The sequence is an arithmetic sequence with
a₁ = -4
d = a₂ - a₁
d = -1 - (-4)
d = -1 + 4
d = 3
an = x
Sn = 437
General formula in arithmetic sequence
Formula to find nth term
an = a₁ + d(n - 1)
Formula to find sum of sequence (sn)
Sn = n/2 (a₁ + an)
We have to make an equation system based on the problem
plug the numbers into the formula
First equation
an = a₁ + d(n - 1)
x = -4 + 3(n - 1)
x = -4 + 3n - 3
x = 3n - 7
Second equation
Sn = n/2 (a₁ + an)
n/2 (a₁ + an) = 437
n/2 (-4 + x) = 437
n(x - 4) = 874
xn - 4n = 874
Solve the equation system by subtitution method
Subtitute x with 3n - 7 in the second equation
xn - 4n = 874
(3n - 7)n - 4n = 874
3n² - 7n - 4n = 874
3n² - 11n - 874 = 0
(3n + 46)(n - 19) = 0
n = -46/3 or n = 19
Because the number of terms shouldn't be negative, -46/3 isn't required, so the value of n is 19.
Solve for x, back to the first equatin
x = 3n - 7
x = 3(19) - 7
x = 57 - 7
x = 50
The solution is 50
Answer:
- 2x + 4 = 36
- 2x = 36-4
- 2x = 32
- x = 32/2
- x = 16
Step-by-step explanation:
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Answer:
B
Step-by-step explanation:
B: it is only a single equation
There are several approaches.
(5/3)x^2 - 5 = 0 has the coefficients a=5/3, b=0 and c = -5.
Thus, the quadratic formula would be appropriate here:
-0 plus or minus sqrt(0^2 - 4(5/3)(-5) )
x = -------------------------------------------------------
2(5/3)
plus or minus sqrt(100/3)
= ------------------------------------
10/3
3 10
= ------* ----------- = sqrt(3) (answer)
10 sqrt(3)
200,000 is ten times 20,000
