What is the common ratio for geometric sequence: 5,15,45,135 ?
1 answer:
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Answer:
1154
Step-by-step explanation:
Perhaps the easiest way to evaluate this numerical expression is to let a calculator do it. Alternatively, we can compute the value from a +1/a.
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<h3>expression</h3>Consider the square of a +1/a:
(a +1/a)^2 = a^2 +2(a)(1/a) +1/a^2 = (a^2 +1/a^2) +2
This means ...
a^2 +1/a^2 = (a +1/a)^2 -2
Similarly, using a^2 for 'a' in the above, we have ...
a^4 +1/a^4 = (a^2 +1/a^2)^2 -2
<h3>numerical value</h3>The value of a +1/a is ...
Then the value of a^2 +1/a^2 is 6^2 -2 = 34
and the value of a^4 +1/a^4 is 34^2 -2 = 1154
