The first, second and third terms of a geometric progression are $$\(2 p+6,-2 p\)$$ and $$\(p+2\)$$ respectively, where $$\(p\)$$ is positive. Find the sum to infinity of the progression. ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................
Exam No：9709_w20_qp_12 Year：2020 Question No：2
Answer:
\((-2 p)^{2}=(2 p+6) \times(p+2)\) or \(\frac{-2 p}{2 p+6}=\frac{p+2}{-2 p}\)
\(\left(2 p^{2}-10 p-12=0\right) p=6\)
\(a=18\) and \(r=-2 / 3\)
\(\left(\mathrm{s}_{\infty}\right)=\) their \(a \div(1-\) their \(r)\)
\(\left(=18 \div \frac{5}{3}\right)\)
\(\left(s_{\infty}=\right) 10.8\)
\(\left(2 p^{2}-10 p-12=0\right) p=6\)
\(a=18\) and \(r=-2 / 3\)
\(\left(\mathrm{s}_{\infty}\right)=\) their \(a \div(1-\) their \(r)\)
\(\left(=18 \div \frac{5}{3}\right)\)
\(\left(s_{\infty}=\right) 10.8\)
Knowledge points:
1.1.3 solve quadratic equations, and quadratic inequalities, in one unknown (By factorising, completing the square and using the formula.)
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.)
1.6.4 use the condition for the convergence of a geometric progression, and the formula for the sum to infinity of a convergent geometric progression.
Solution:
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