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:
5/9-1/9=4/9
Step-by-step explanation:
5/9 chose basketball or soccer. 1/9 chose basketball.
<h3>answer is 4/9</h3>
Make two shapes out of it.
The bottom is a rectangle 14 x 5 = 70 square cm
The top is a triangle 1/2 x 12 x 5 = 30 square cm
Total area = 70 + 30 = 100 square cm
Answer: First Option : Sₙ= n/2(a₁ + aₙ)
Step-by-step explanation:
The nth partial sum of an arithmetic sequence or the sum of the first n terms of the arithmetic series can be defined as the sum of a finite number of term in an arithmetic sequence.
It is calculated using the formula:
Sₙ= n/2(a₁ + aₙ)
Where :
a₁ = First term
aₙ = last term
n = number of terms
