Answer:
[tex]\bold{a_1 = -42.65}\\\\\bold{d=14.7}[/tex]
Step-by-step explanation:
The sum of the first 10 terms of an arithmetic sequence is:
[tex]S_{10}=a_1+a_2+...+a_{10}=\dfrac{a_1+a_{10}}{2}\cdot10=\dfrac{2a_1+(10-1)d}{2}\cdot10[/tex]
[tex]\dfrac{2a_1+(10-1)d}{2}\cdot10=235\\\\(2a_1+9d)\cdot5=235\\\\2a_2+9d=47[/tex]
the sum of the second 10 terms is: a₁₁ + a₁₂+...+ a₂₀
And the sum of the first 20 terms of an arithmetic sequence is:
[tex]S_{20}=a_1+a_2+...+a_{10}+a_{11}+...+a_{20}=\dfrac{2a_1+(20-1)d}{2}\cdot10[/tex]
so the sum of the second 10 terms is:
[tex]a_{11}+a_{12}+...+a_{20}=S_{20}-S_{10}[/tex]
Therefore we have:
[tex]\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[/tex]
and:
[tex]2a_1+9\cdot14.7=47\\\\2a_1+132.3=47\\\\2a_1=-85.3\\\\a_1=-42,65[/tex]
