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Svetlanka [38]
3 years ago
8

Determine the common ratio and find the next three terms of the geometric sequence.

Mathematics
1 answer:
12345 [234]3 years ago
3 0

Answer:

  • a_{4} =0.875
  • a_5=-0.4375
  • a_6=0.21875

Step-by-step explanation:

As we know that a geometric sequence does have the common ratio whoch is defined as the ratio of a term to the preceding term.

This common ratio is normally denoted by the 'r'.

As the given sequence is

-7, 3.5, -1.75 ...

So,

r=\frac{3.5}{-7}=-0.5, r=-\frac{1.75}{3.5}=-0.5

To find the nth term of a geometric sequence we use the formula:

a_{n} =a_{1} r^{n-1}

where,

r is the common ratio and a_{1} being the first term.

So, the next three terms i.e. a_{4}, a_{5} and a_{6} can be obtained by substituting the values of n = 4, n = 5 and n = 6 respectively in a_{n} =a_{1} r^{n-1}.

As

a_{1} =-7

r=-0.5

a_{n} =a_{1} r^{n-1}

So,  a_{4}, a_{5} and a_{6} can be obtained by substituting the values of n = 4, n = 5 and n = 6 respectively in a_{n} =a_{1} r^{n-1} when a_{1} =-7 and r=-0.5.

a_{4} =a_{1} r^{4-1}

a_{4} =(-7) r^{3}

a_{4} =(-7) (-0.5)^{3}

a_{4} =0.875

a_{5} =a_{1} r^{5-1}

a_{5} =(-7) r^{4}

a_{5} =(-7) (-0.5)^{4}

a_5=-0.4375

a_{6} =a_{1} r^{6-1}

a_{6} =(-7) r^{5}

a_{6} =(-7) (-0.5)^{5}

a_6=0.21875

Therefore,

  • a_{4} =0.875
  • a_5=-0.4375
  • a_6=0.21875

Keywords: geometric sequence , common ratio

Learn more about geometric sequence from brainly.com/question/12652555

#learnwithBrainly

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