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What is the 7th term of the geometric sequence where a1 equals 1024 and a4 equals -16?
Given:
a1=1024
a4=-16
Find: a7
Formula:
an=a1rn-1
To get the ratio, r:
a4=a1r4-1
-16=1024r4-1
-16=1024r3
-16/1024=1024/1024r3
-1/64=r3
-1/4=r
Substiture r=1/4 to the formula to get a7
a7=a1r7-1
=a1r6
=1024(-1/4)6
=1024(1/4096)
=1/4
=0.25
Therefore the 7th term=0.25
FromC2H5.OH:
The fourth term is the geometric mean of the first and seventh terms and is therefore the square root of their product;
this means that -16 squared = 1024 x a7
ie a7 = 256/1024 = 0.25
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