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 sum of the first 16 terms when $$$\theta=\frac{1}{3} \pi$$$. ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_13 Year：2020 Question No：8(b)(ii)

Answer:

Use of $S_{16}=\frac{16}{2}[2 a+15 d]$
With both $a=\frac{3}{4}$ and $d=-\frac{9}{16}$
$S_{16}=-55 \frac{1}{2}$

Knowledge points:

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.)

Answer:

Knowledge points:

Solution:

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