Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
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]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.