1 year ago

Find the sum of the primes between 100 and 200, inclusive, that are 1 or 2 more than a perfect square.

Mathematics

1 answer:

ira [324]1 year ago

6 0

Answer:

298

Step-by-step explanation:

All perfect squares from 100-200 inclusive:

100, 121, 144, 169, 196

100+1=101, 101 is prime

121+2=123, 123=41*3 so its not prime

144+1=145 145=29*5 so its not prime

169+2=171 171=9*19 so its not prime

196+1=197, 197 is prime

101+197=298

Notice that I excluded all even numbers because they are obviously composite.

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A sequence is defined recursively using the formula f(n+1)=-0.5f(n). If the first term of the sequence is 120, what is f(5)?

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Answer:
f (5) = 7.5

Explanation:
The function given is:
f (n+1) = -0.5 f (n)

We are also given that:
first term is 120
This means that:
f (1) = 120

We will get the other terms by substitution as follows:
f (2) = -0.5 f (1) = -0.5(120) = -60
f (3) = -0.5 f(2) = -0.5(60) = 30
f (4) = -0.5 f(3) = -0.5(30) = -15
f (5) = -0.5 f(4) = -0.5(-15) = 7.5

Therefore, f (5) = 7.5

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