# 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.

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