Question

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

Answer 1

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

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