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
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56 dived by 2 equals 28. 28=green ribbon. Brown ribbon is 4 times as long. 28 times 4 equals 112. The brown ribbon is 112 cm long.
Answer:
3-i
Step-by-step explanation:
1-5i + 2 +4i
We add the real parts
1+2 =3
We add the imaginary parts
-5i + 4i = -1i
The complex number is
3-i
Answer: 120
Step-by-step explanation:
20 divided by 20 is 1.
We have to multiply this by 120.
120 x 1 = 120. It is the answer.
Answer: 
Step-by-step explanation:
For this exercise it is important to remember the following:
The constant of proportionality, which is represented as "k", describe the constant ratio of two quantities that are proportional (the independent and dependent variables).
In this case we know that the independent quantity represents the total members of the band and the dependent quantity represents the woodwind members of the band.
Since the band consists of 3 woodwinds for every 7 members of the band, we can conclude that the constant of proportionality for this relationship is:
