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:
94 cm.
Step-by-step explanation:
Perimeter = 25 + 2(10) + + 2(12) + 25
= 50 + 20 + 24
= 94 cm.
Answer:
AA similarity
Step-by-step explanation:
Using angle sum theorem, you can clearly find out the missing angles on the left and right triangles are 40° and 50° respectively.
Therefore, by using any two angles in the triangles, you can prove they are similar by AA similarity.
Answer:
140,120
Step-by-step explanation:
sum of angles in a quadrilateral =360
sum of the 1st two angles=60+40=100
360-100=260
the ratio of the remaining angles 7:6
therefore:
=140
for the second angle
260-140=120
Answer:
i think it's either 31 or 28
