How do you write the first five terms of the geometric sequence #a_1=3, r=sqrt5#?
a GP is generated by multiplying the previous term by the common ration.
Starting with the first term given.
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To find the first five terms of the geometric sequence given (a_1 = 3) and (r = \sqrt{5}), we use the formula for the (n)th term of a geometric sequence:
[a_n = a_1 \times r^{(n-1)}]
Substituting the given values:
For (n = 1): (a_1 = 3)
For (n = 2): (a_2 = 3 \times (\sqrt{5})^{(2-1)})
For (n = 3): (a_3 = 3 \times (\sqrt{5})^{(3-1)})
For (n = 4): (a_4 = 3 \times (\sqrt{5})^{(4-1)})
For (n = 5): (a_5 = 3 \times (\sqrt{5})^{(5-1)})
Calculating these values:
For (n = 1): (a_1 = 3)
For (n = 2): (a_2 = 3 \times \sqrt{5})
For (n = 3): (a_3 = 3 \times 5)
For (n = 4): (a_4 = 3 \times (\sqrt{5})^3)
For (n = 5): (a_5 = 3 \times (\sqrt{5})^4)
Simplify:
For (n = 1): (a_1 = 3)
For (n = 2): (a_2 = 3\sqrt{5})
For (n = 3): (a_3 = 15)
For (n = 4): (a_4 = 3\sqrt{5^3})
For (n = 5): (a_5 = 3\sqrt{5^4})
So, the first five terms of the geometric sequence are (3), (3\sqrt{5}), (15), (15\sqrt{5}), and (75).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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