Find the common ratio of the following geometric sequence. If necessary, use the slash bar ( / ) to enter a fraction. Reduce fra
ctions to their lowest terms.,
2/5 , -4/15 , 8/45 , -4/15 , -8/45
1 answer:
We have that
<span>2/5 , -4/15 , 8/45 , -4/15 , -8/45
we know that
</span><span>A geometric sequence is defined by
a(n + 1) = r*a(n)
so
r = a(n + 1) / a(n)</span>
Let
a1=2/5
a2=-4/15
a3=8/45
a2/a1=(-4/15)/(2/5)=-20/30------> -2/3
a3/a2=(8/45)/(-4/15)=-20/30------> -30/45--------> -2/3
<span>the common ratio is
</span>r=-2/3
calculate
a4=r*a3---------> (-2/3)*8/45-----> -16/135
a5=r*a4--------> (-2/3)*(-16/135)-----> 32/405
the correct geometric sequence is
2/5 , -4/15 , 8/45 , -16/135 , 32/405, .....
the answer is
the common ratio is r=-2/3
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