We appreciate your visit to Find the sum of the sequence 227 225 223 221 209. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
2180 (option A)
Explanation:common difference = next term - previous term
d = 225 - 227
d = -2
The formula for sum of sequence of an arithmetic progression:
[tex]S_n=\frac{n}{2}\lbrack2a_1+(n-1)d\rbrack[/tex][tex]\begin{gathered} \\ a_n=a_1+(n-1)d \\ S_n=\frac{n}{2}(a_1+a_n) \\ a_n\text{ = 209, }a_{1\text{ }}=\text{ 227} \end{gathered}[/tex][tex]\begin{gathered} S_n\text{ =}\frac{n}{2}(209\text{ + 227)} \\ S_n\text{ =}\frac{n}{2}(436\text{)} \end{gathered}[/tex][tex]\begin{gathered} To\text{ get n, we would apply the formula:} \\ a_n=a_1\text{ + (n-1)d} \\ a_n\text{ = last term = 209} \\ n\text{ = ?, d = -2, }a_1=\text{ 227} \\ 209\text{ = 227 + (n - 1)(-2)} \\ \end{gathered}[/tex][tex]\begin{gathered} 209\text{ = 227 -2n + 2} \\ 209\text{ - 227 = -2n + 2} \\ -18\text{ = -2n + 2} \\ -18-2\text{ = -2n} \\ -20\text{ = -2n} \\ n\text{ = -20/-2} \\ n\text{ = 10} \end{gathered}[/tex][tex]\begin{gathered} \text{The sum of the sequence = S}_n\text{ = }\frac{n}{2}(436) \\ S_n=\frac{10}{2}\times436 \\ S_n\text{ = 2180 (option A)} \end{gathered}[/tex]Thanks for taking the time to read Find the sum of the sequence 227 225 223 221 209. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
