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A geometric sequence has all its terms positive. The first term is 7 and the third term is 28.

THIS IS FOR MATHS STUDIES, NOT MATHS SL The question is from the 2014 specimen paper First, find the common ratio:U1 = 7U3 = 28 (Identify Formula): Un = U1 x r^n-1 U3 = 7xr^3-1 28 = 7xr^2 r = 2 Then, find th...
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Answered by Lottie W. • Maths tutor
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Prove by mathematical induction that (2C2)+(3C2)+(4C2)+...+(n-1C2) = (nC3).

Firstly, show the equation is true for n = 3 (as this is the samllest n that nC3 is defined): LHS = (2C2) = 1 = (3C3) = RHStherefore, true for n=3. Then assume true for n = k:(2C2)+(3C2)+(4C2)+...+(k-1C2) = ...
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Answered by Henry X. • Maths tutor
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log_10⁡((1/(2√2))*(p+2q))=(1/2)(log_10⁡p+log_10⁡q),p,q>0,find p in terms of q.

log 10 [(1/2√2) (p+2q)]=(1/2)(log 10 p+log 10 q)log 10 [(1/2√2) (p+2q)]=(1/2)(log 10 pq)log 10 [(1/2√2) (p+2q)]=log 10 (pq) 1/2 (1/2√2) (p+2q)=(pq) 1/2 (p+2q) 2 =8pqp 2 +4pq+4q 2 =8pqp 2 -4pq+4q 2 =0(p-2q)=0...
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Answered by Henry X. • Maths tutor
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Can you explain the approach to solving IB maths induction questions?

Proof by maths induction is a type of proof used in mathematical analysis to demonstrate that a certain expression or statement P(n) involving an arbitrary neutral number n is true for all n belonging to N. ...
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Answered by Vlad B. • Maths tutor
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Finding complex numbers using DeMoivre's Theorem

Find the cube roots of 2 1/2 cis(pi/4) 2 1/2 cis(pi/4+ 2pi k), for every integer k By DeMoivre: 2 1/2 1/3 cis((pi/4+ 2pi k)/3) 3 2 1/6 cis(pi/12+ 2/3 pi *k) Taking k=0,1,2 gives the three cube roots:z 1 = 2 ...
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Answered by Lisa R. • Maths tutor
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