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the sum of the first 10 terms of arithmetic sequence 530. What is the first terms if the last term is 80?

Sagot :

Answer:

first term = 26

Step-by-step explanation:

We can find the first term of the arithmetic sequence with the sum of 530 and the last term of 80 by using this formula:

[tex]\boxed{S_n=\frac{n}{2} (U_1+U_n)}[/tex]

where:

  • [tex]S_n=\texttt{sum of n number of terms}[/tex]
  • [tex]n=\texttt{number of terms}[/tex]
  • [tex]U_1=\texttt{first term}[/tex]
  • [tex]U_n=\texttt{n-th term (last term)}[/tex]

Given:

  • [tex]S_n=530[/tex]
  • [tex]n=10[/tex]
  • [tex]U_n=80[/tex]

Then:

[tex]\begin{aligned}S_n&=\frac{n}{2} (U_1+U_n)\\\\530&=\frac{10}{2} (U_1+80)\\\\U_1+80&=530\div5\\\\U_1&=106-80\\\\\bf U_1&=\bf26\end{aligned}[/tex]

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