3 years ago

Simplify the ratio 19:114

Mathematics

1 answer:

masha68 [24]3 years ago

8 0

$19:114 = \frac{19}{114}$ ÷ $\frac{19}{19} = \frac{1}{6} = 1:6 \ \textless \ -answer$

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the sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms is -165. Find the 18th term of

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Answer:

Step-by-step explanation:

$S_{10}=\dfrac{2a_1+d(10-1)}{2}\cdot 10\\\\\dfrac{2a_1+9d}{2}\cdot 10=-60\\\\\dfrac{2a_1+9d}{2}=-6\\\\2a_1+9d=-12\\\\2a_1=-12-9d\\\\\\S_{15}=\dfrac{2a_1+d(15-1)}{2}\cdot 15\\\\\dfrac{2a_1+14d}{2}\cdot 15=-165\\\\\dfrac{2a_1+14d}{2}=-11\\\\2a_1+14d=-22\\\\-12-9d+14d=-22\\\\ 5d=-10 \\\\ d=-2\\\\\\2a_1=-12-9(-2)=-12+18=6\\\\a_1=3\\\\\\ a_{18}=a_1+17d=3+17(-2)=3-34=-31$