The first term of a progression is $$\(\sin ^{2} \theta\)$$, where $$\(0< \theta< \frac{1}{2} \pi\)$$. The second term of the progression is $$\(\sin ^{2} \theta \cos ^{2} \theta\)$$ It is now given instead that the progression is arithmetic. Find the common difference of the progression in terms of $$\(\sin \theta\)$$. ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................

Mathematics
IGCSE&ALevel
CAIE
Exam No:9709_s20_qp_13 Year:2020 Question No:8(b)(i)

Answer:

\(d=\sin ^{2} \theta \cos ^{2} \theta-\sin ^{2} \theta\)
\(\sin ^{2} \theta\left(\cos ^{2} \theta-1\right)\)
\(-\sin ^{4} \theta\)

Knowledge points:

1.5.4 use the identities
1.6.3 use the formulae for the nth term and for the sum of the first n terms to solve problems involving arithmetic or geometric progressions (Including knowledge that numbers a,b,c are 'in arithmetic progression' if 2 b=a+c (or equivalent) and are 'in geometric progression' if (or equivalent) (Questions may involve more than one progression.)

Solution:

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