Arithmetic Series, Geometric Sequence

Mathematics
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May 6th, 2015

14. Sum from 1 to 13 of (15*k-4) = [a(1)+ a(13)]*13/2= [15-4+15*13-4]*13/2 = [15*14-8]*13/2= [15*7-4]*13

= [105-4]*13=101*13= 1313

15. a(3)=16, a(5)=64.

In geometric series: a(n+k)/a(n)=aq^(n-1+k)/[aq^(n-1)]=q^k

Here: n+k=5, n=3 => k=2, q^2=64/16=4 => q=2

a(7)=a(5)*q^2=64*4=256

May 6th, 2015

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