Please help me solve this?
1 answer:
Answer:
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
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<em>Comment on the rule of exponents</em>
You can see where the rule comes from when you consider that an exponent signifies repeated multiplication.
x² = x·x . . . . . . the 2 signifies that x is a factor 2 times
x³ = x·x·x . . . . the 3 signifies that x is a factor 3 times
The product of these is ...
(x²)(x³) = (x·x)(x·x·x) = x·x·x·x·x = x⁵ = x²⁺³
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ARITHMETIC CHECK: A sequence is said to be arithmetic if any two consecutive terms differ by the same constant.
So, the test to check if a series is arithmetic is to compute consecutive differences, and see if they all return the same number.
If we subtract the first two terms, we have . If we subtract the third and second terms, we have
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These two differences returned two different values, so the series is not arithmetic.
GEOMETRIC CHECK: A sequence is said to be geometric if any two consecutive terms are in the same ratio.
So, the test to check if a series is geometric is to compute consecutive ratios, and see if they all return the same number.
If we divide the first two terms, we have
If we divide the third and second terms, we have
Finally, if we divide the last two terms we have
So, all ratios return the same number. This means that the series is geometric, and the common ratio is 1/2