Mathematics: Given u1 = 56 and un = 0.7un-1, find s12. round to the nearest hundredth a) 181.39 b) 184.08 c) 185.32 d) 186.66

Given u1 = 56 and un = 0.7un-1, find s12. round to - id156071123848494, bestsonever698

MaTh8809

10.01.2022

184.08

Step-by-step explanation:

$u_{1},u_{2},u_{3}.....u_{n}$ form a sequence exhibiting the following property :

$u_{1}=56;u_{n}=0.7u_{n-1}$

On rewriting, $\dfrac{u_{n}}{u_{n-1}}=0.7$ ⇒ Ratio of consecutive terms is a constant. Hence, the sequence is a Geometric Progression.

The ratio 0.7 is the common ratio . First term = $u_{1}=56$ .

Sum of terms of a Geometric progression is given by

$S_{n}=a\times\dfrac{1-r^{n}}{1-r}$ when .

$S_{12}=56\times(\dfrac{1-(0.7)^{12}}{1-0.7})=56\times\dfrac{0.986}{0.3}=184.083$

∴ $S_{12}$ to the nearest hundreth is 184.08

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