Determine the number of terms for the following geometric sequence:
a) 2, 4, 8,.........1024
Full solution please.
Determine the number of terms for the following geometric sequence:
a) 2, 4, 8,.........1024
Full solution please.
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The sequence is of relation ship
2 ^ N where N = 1 to X
So there for
2 ^ X = 1024
and thus X = 10
Therefore there are 10 terms in the series.
So far as I can remeber this in not the correct sequence notation, but the answer is correct, no?
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2^1,2^2...............2^10
so 1024 is 10th term
therfore total 10 terms in the series
2^1,2^2...............2^10
so 1024 is 10th term
therfore total 10 terms in the series
In the geometric Sequence ,
First Term is 2. Second term = 4 (2 * 2=> 2 to power 2)
Third term is 8(2*2*2 => 2 to power 3). From this above pattern Number of term is equal to power of 2.
here the last term is 1024(2 to power10 )
Therefore 1024 is the 10th term .
Therefore the number of term in Geometric Sequence = 10
The formula for Nth term of a G.P. series is
T(N)=a*r^(N-1), where a= first term, r= common ratio, T(N)=last term
=> 1024=2*2^(N-1)
=> 2^(N-1)=512
=> 2^(N-1)=2^9
=> (N-1)=9
=> N=10.
2 ^ N where N = 1 to X
So there for
2 ^ X = 1024
and thus X = 10
Therefore there are 10 terms in the series.
hi
2*2=4*2=8*2=16 last number is sereis is 512*2=1024 ten time of row is multiply by 2.
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