What is the sum of the first ten terms of the sequence 4, -12, 36, -108 . . . ?Select one:a.-78,732b.-59,048c.118,096d.59,048

Question

What is the sum of the first ten terms of the sequence 4, -12, 36, -108 . . . ?

Select one:

a. -78,732
b. -59,048
c. 118,096
d. 59,048

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Solution

This is a geometric sequence where the common ratio is -3 (each term is -3 times the previous term). The sum S of the first n terms of a geometric sequence can be found using the formula:

S = a * (1 - r^n) / (1 - r)

where: a is the first term of the sequence, r is the common ratio, and n is the number of terms.

Substituting the given values into the formula:

S = 4 * (1 - (-3)^10) / (1 - (-3))

S = 4 * (1 - 59049) / 4

S = 4 * -59048 / 4

S = -59048

So, the sum of the first ten terms of the sequence is -59,048 (option b).

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What is the sum of the first ten terms of the sequence 4, -12, 36, -108 . . . ?Select one:a.-78,732b.-59,048c.118,096d.59,048

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