SOLUTION: please help solve these two problems: sequence 4,8,16,32,64,128… d=2 a sub 1=4 prob #1: a(3) what is a? is that the same as a sub exponent 1 which is 4? prob #2: a(1)+a(7)

Algebra ->  Sequences-and-series -> SOLUTION: please help solve these two problems: sequence 4,8,16,32,64,128… d=2 a sub 1=4 prob #1: a(3) what is a? is that the same as a sub exponent 1 which is 4? prob #2: a(1)+a(7)       Log On


   



Question 944648: please help solve these two problems:
sequence 4,8,16,32,64,128…
d=2
a sub 1=4
prob #1: a(3) what is a? is that the same as a sub exponent 1 which is 4?
prob #2: a(1)+a(7)
Thank you

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
please help solve these two problems:
sequence 4,8,16,32,64,128…
Note:: This is a Geometric Sequence
r = 8/4 = 2
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a(1) = 4
=======
prob #1: a(3) what is a?
a(3) = a*r^2 = 4*2^2 = 16
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prob #2: a(1)+a(7) = 4 + 4*r^6 = 4 + 4*2^6 = 4+4*64 = 4+256 = 260
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Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

sequence 4,8,16,32,64,128…
d=2 ---> common multiplier
a sub 1=4 => a sub 1=a%5B1%5D which is first term in sequence and first term is 4
prob #1:+a%5B3%5D => third term which is 16; so, a%5B3%5D+=16
prob #2:+a%5B1%5D%2Ba%5B7%5D+=4%2Ba%5B7%5D+
=> we need general formula to find a%5B7%5D
sequence 4,8,16,32,64,128…using common multiplier could be written as 2%5E2, 2%5E3,+2%5E4, 2%5E5, 2%5E6..... 2%5E%28n%2B1%29
so, general formula is:
a%5Bn%5D+=+2%5E%28n%2B1%29 (for all terms given) where n is the number of the term
now find a%5B7%5D
a%5B7%5D+=+2%5E%287%2B1%29+
a%5B7%5D+=+2%5E8
a%5B7%5D+=+256
and +a%5B1%5D%2Ba%5B7%5D+=4%2Ba%5B7%5D+ will be
+a%5B1%5D%2Ba%5B7%5D+=4%2B256+
+a%5B1%5D%2Ba%5B7%5D+=260+