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zzz [600]
3 years ago
11

The 9th term of arithmetic sequence is 37 and 16th term is 65 find the 100th team.​

Mathematics
1 answer:
Irina18 [472]3 years ago
5 0

Answer:

<h2>           a₁₀₀ = 385</h2>

Step-by-step explanation:

The nth term of arithmetic sequence is   a_n=a_1+d(n-1)

So:

     a_9=a_1+d(9-1)\\\\37=a_1+8d\\\\a_1=37-8d\\\\\\a_{16}=a_1+d(16-1)\\\\65=a_1+15d\\\\65=37-8d+15d\\\\28=7d\\\\d=4\\\\a_1=37-8\cdot4=5\\\\\\a_{100}=a_1+d(100-1)=5+4\cdot95=385

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<h3>How to determine the function (f - g)(x)?</h3>

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<u>Complete question</u>

Cynthia was offered two different jobs for the summer. working as a camp counselor, she will earn $15 per hour plus an additional $25 bonus. her earnings after x hours can be represented by the function f(x) = 15x + 25. working as a lifeguard, Cynthia will earn $10 per hour and an additional $50 bonus. her earnings after x hours can be represented by the function g(x) = 10x + 50. the arithmetic operation (f - g)x can be used to determine the difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours. what is the function (f - g)x?

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