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Sagot :
Answer:
the sum of first 50 terms = 3725
Step-by-step explanation:
To find the sum of the first 50 terms for arithmetic sequence of 3n-2, we use this formula:
[tex]\boxed{S_n=\frac{n}{2} (U_1+U_n)}[/tex]
where:
- [tex]S_n=\texttt{sum of the first n terms}[/tex]
- [tex]n=\texttt{number of terms}[/tex]
- [tex]U_1=\texttt{the 1st term}[/tex]
- [tex]U_n=\texttt{the n-th term}[/tex]
Before we can find S₅₀, we have to find U₁ and U₅₀ by using the given sequence formula Uₙ = 3n - 2:
[tex]\begin{aligned}U_1&=3(1)-2\\&=1\end{aligned}[/tex]
[tex]\begin{aligned}U_{50}&=3(50)-2\\&=148\end{aligned}[/tex]
Now, we can find S₅₀:
[tex]\begin{aligned} S_n&=\frac{n}{2} (U_1+U_n)\\\\S_{50}&=\frac{50}{2} (1+148)\\\\&=\bf 3725\end{aligned}[/tex]
Answer:
Sum of the first 50 terms of the arithmetic sequence given by the formula [tex]a_n=3n-2 $ is $ \boxed{\;\;\; 3,725\;\;\;}[/tex]
Step-by-step explanation:
The sum of an arithmetic series for the first n terms is given by the formula
[tex]$S_n = \dfrac {n}{2} \left (a_1 + a_n)$where \\$a_1 = $ first term\\$a_n = $ nth term\\$n = $ number of terms[/tex]
Given the formula for arithmetic sequence as
[tex]a_n = 3n - 2[/tex]
the first term is
[tex]a_1 = 3(1) - 2 = 3 - 2 = 1[/tex]
the 50th term is
[tex]a_{50} = 3(50) - 2 = 150 - 2 = 148[/tex]
and, number of terms is
[tex]n = 50[/tex]
Using the formula provided for the sum of arithmetic sequence we get
[tex]S_{50} = \dfrac{50}{2} (1 + 148)[/tex]
[tex]S_{50} = 25 (149)[/tex]
[tex]S_{50} = 3,725[/tex]
Answer
Sum of the first 50 terms of the arithmetic sequence given by the formula [tex]a_n=3n-2 $ is $ 3,725[/tex]
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