The 24th term is 152
Step-by-step explanation:
The formula of the nth term of an arithmetic sequence is:
, where
- a is the first term
- d is the common difference between consecutive terms
The third term means n = 3
∵ 
∴ 
∵ 
= 5
- Equate the right hand sides of the third term
∴ a + 2d = 5 ⇒ (1)
The fifth term means n = 5
∵ 
∴ 
∵ 
= 19
- Equate the right hand sides of the fifth term
∴ a + 4d = 19 ⇒ (2)
Now we have a system of equations to solve it
Subtract equation (1) from equation (2) to eliminate a
∴ 2d = 14
- Divide both sides by 2
∴ d = 7
- Substitute the value of d in equation (1) to find a
∵ a + 2(7) = 5
∴ a + 14 = 5
- Subtract 14 from both sides
∴ a = -9
The twenty fourth term means n = 24
∵ a = -9 and d = 7
- Substitute the values of a and d in the formula of the nth term
∴ 
∴ 
∴ 
∴ 
The 24th term is 152
Learn more:
You can learn more about the arithmetic sequence in brainly.com/question/7221312
#LearnwithBrainly
The function modelled by the height (x) of the tree is as follows:
y - 180 = (368 - 180)/(7 - 3) (x - 3)
y - 180 = 47(x - 3) = 47x - 141
y = 47x - 141 + 180 = 47x + 39
Therefore, after 10 years, the tree will be 47(10) + 39 = 470 + 39 = 509 cm tall
Answer:
10
Step-by-step explanation:
Substitute 1 in place of x and the result is -4.
Again substitute 3 in place of x and the result is 6.
Change=6-(-4)=10
Answer:
D. Dilate rectangle A by a scale factor of 3 with the center of dilation at the origin and rotate it 90° clockwise about the origin.
Step-by-step explanation:
The coordinates of triangle A are (-2,1) , (1,1), (1,-1) and (-2, -1) while that of triangle B are (-3, 6), (3, 6), (3, -3) and (-3, 3).
To transform A to be we need a combination of two transformations, and that is dilation and rotation.
If A is dilated by a scale factor three through the origin as the center of dilation and then rotated through 90° clockwise with the origin as the center of origin, then rectangle B will be obtained.
