A number line is shown below. What point represents the approximation of 24 on the number JK L M line 1 + 2 N 3 5 6 7 8 9 10 Poi
nt Point K Point L Point M
2 answers:
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The first term will be 3 and the sum of the first 9 terms will be 81.
<h3>What is Arithmetic progression?</h3>The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
Natural number = 1,2,3,4,5,6,7,8...
Given,
Six terms as 10.5
So,
a₆ = 10.5
Common difference(d) = 1.5
The nth term of an AP is given by
= a + (n-1)d
So,
a₆ = a + (6-1)d
10.5 = a + 5(1.5)
a = 3
Now,
The Sum of n terms is given by
S = n/2[2a + (n-1)d]
S = 9/2[6 + 8(1.5)]
S = 81
Hence the first term will be 3 and the sum of 9 terms will be 81.
For more about Arithmetic progression
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Answer:
The fifth root is 2[cos(56°) + i sin(56°)]
Step-by-step explanation:
* To solve this problem we must revise De Moiver's rule
- In the complex number with polar form
∵ z = r(cosФ + i sinФ)
∴ z^n = r^n(cos(nФ) + i sin(nФ))
* In the problem
- The fifth root means z^(1/5)
- We can put 32 as a form a^n
∵ 32 = 2 × 2 × 2 × 2 × 2 = 2^5
∴ z = 2^5[cos(280°) + i sin(280°)]
* Lets find z^(1/5)
∴ z^(1/5) = 2[cos(56) + i sin(56)]
* The fifth root of 32[cos(280°) + i sin(280°)] is 2[cos(56°) + i sin(56°)]