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marishachu [46]
2 years ago
5

Consider a geometric sequence with a first term of 4 and a fourth term of -2.916.

Mathematics
1 answer:
Orlov [11]2 years ago
4 0

Answer:

a) Find the common ratio of this sequence.

Answer: -0.82

b) Find the sum to infinity of this sequence.

Answer: 2.2

Step-by-step explanation:

nth term in geometric series is given by 4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{0.549} \\r = 0.82

where

a is the first term

r is the common ratio and

n is the nth term

_________________________________

given

a = 4

4th term = -2.196

let

common ratio of this sequence. be r

4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{-0.549} \\r = -0.82

a) Find the common ratio of this sequence.

answer: -0.82

sum of infinity of geometric sequence is given by = a/(1-r)

thus,

sum to infinity of this sequence = 4/(1-(-0.82) = 4/1.82 = 2.2

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