Mathematics: 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 the sequence

the sum of the first ten terms of a linear sequence

Ответ:

hannahdrees0731

17.05.2021

a₁₈ = - 31

Step-by-step explanation:

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

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Ответ:

asiaboo37

17.01.2020

Mathematics

The sun is 9.2549 x 10^-7 miles from the earth

NOTE: I don't know how many significant figures you are needing/given.

Step-by-step explanation:

The earth is 92.549 million miles from the sun.

92 549 000 miles from the sun.

Move the decimal place left until you're right after the first significant figure.

9.2549 x 10^-7

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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 the sequence

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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 the sequence​

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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 the sequence