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Aleksandr [31]
3 years ago
14

Please help me!!!! with both​

Mathematics
1 answer:
loris [4]3 years ago
6 0

Answer:

Part 11)  a_n=a_{n-1}-16, a_1=17

Part 2) 4+3i

Step-by-step explanation:

Part 11) write a recursive rule for the sequence

17,1,-15,-31,...

Let

a_1=17\\a_2=1\\a_3=-15\\a_4=-31

we know that

a_2-a_1=1-17=-16 ----> a_2=a_1-16

a_3-a_2=-15-1=-16 ----> a_3=a_2-16

a_4-a_3=-31-15=-16 ----> a_4=a_3-16

This is an arithmetic sequence

In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference (d).

In this problem the common difference is equal to d=-16

therefore

A recursive rule for the sequence is

a_n=a_{n-1}+d

substitute the value of d

a_n=a_{n-1}-16

where

a_1=17

Part 12) What is the complex conjugate of 4-3i?

we know that

The <u><em>complex conjugate</em></u> of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign

so

we have that

the real part of the given number is 4 and the the imaginary part is -3i

so

the imaginary part equal in magnitude but opposite in sign is +3i

therefore

the complex conjugate of the given number is equal to

4+3i

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