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Consider a sequence of numbers given by the definition #c_1=2, c_i=c_(i-1)*3#, how do you write out the first 4 terms and how do you find the value of #c_4-c_2#?

Answer 1

Elias Ackerman

#c_4 - c_2 = 48#.

The terms can be obtained as follows.

#c_2 = c_(2 - 1) * 3 = c_1 * 3 = 2 * 3 = 6#

#c_3 = c_(3- 1) * 3 = c_2 * 3 = 6 * 3 = 18#

#c_4 = c_(4- 1) * 3 = c_3 * 3 = 18 * 3 = 54#

Thus, the value of #c_4 - c_2# is #54 - 6 = 48#.

Hopefully this helps!

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Answer 2

Greyson Brown

The first four terms of the sequence are: ( c_1 = 2, c_2 = 2 \times 3 = 6, c_3 = 6 \times 3 = 18, c_4 = 18 \times 3 = 54 ). To find the value of ( c_4 - c_2 ), substitute the values: ( c_4 - c_2 = 54 - 6 = 48 ).

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Answer from HIX Tutor

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.