3 years ago

Can you answer this one question please

Mathematics

1 answer:

Fofino [41]3 years ago

5 0

Answer:

(3, 2) is the intersection point of the graphs of

x + y = 5 and x - y = 1.

Step-by-step explanation:

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3 years ago

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The sum of the first 10 terms of an arithmetic sequence is 235 and the

Degger [83]

Answer:

$\bold{a_1 = -42.65}\\\\\bold{d=14.7}$

Step-by-step explanation:

The sum of the first 10 terms of an arithmetic sequence is:

$S_{10}=a_1+a_2+...+a_{10}=\dfrac{a_1+a_{10}}{2}\cdot10=\dfrac{2a_1+(10-1)d}{2}\cdot10$

$\dfrac{2a_1+(10-1)d}{2}\cdot10=235\\\\(2a_1+9d)\cdot5=235\\\\2a_2+9d=47$

the sum of the second 10 terms is: a₁₁ + a₁₂+...+ a₂₀

And the sum of the first 20 terms of an arithmetic sequence is:

$S_{20}=a_1+a_2+...+a_{10}+a_{11}+...+a_{20}=\dfrac{2a_1+(20-1)d}{2}\cdot10$

so the sum of the second 10 terms is:

$a_{11}+a_{12}+...+a_{20}=S_{20}-S_{10}$

Therefore we have:

$\dfrac{2a_1+(20-1)d}{2}\cdot10-\dfrac{2a_1+(10-1)d}{2}\cdot10=735\\\\(2a_1+19d)\cdot5-(2a_1+9d)\cdot5=735\\\\2a_1+19d-(2a_1+9d)=147\\\\10d=147\\\\d=14.7$

and:

$2a_1+9\cdot14.7=47\\\\2a_1+132.3=47\\\\2a_1=-85.3\\\\a_1=-42,65$

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