Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Given:
In an arithmetic sequence,
[tex]a_1=2[/tex]
[tex]a_i=a_{i-1}-3[/tex]
To find:
The sum of the first 335 terms in the given sequence.
Solution:
The recursive formula of an arithmetic sequence is:
[tex]a_i=a_{i-1}+d[/tex] ...(i)
Where, d is the common difference.
We have,
[tex]a_i=a_{i-1}-3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]d=-3[/tex]
The sum of first i terms of an arithmetic sequence is:
[tex]S_i=\dfrac{i}{2}[2a+(i-1)d][/tex]
Putting [tex]i=335,a=2,d=-3[/tex], we get
[tex]S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)][/tex]
[tex]S_{335}=\dfrac{335}{2}[4+(334)(-3)][/tex]
[tex]S_{335}=\dfrac{335}{2}[4-1002][/tex]
[tex]S_{335}=\dfrac{335}{2}(-998)[/tex]
On further simplification, we get
[tex]S_{335}=335\times (-499)[/tex]
[tex]S_{335}=-167165[/tex]
Therefore, the sum of the first 335 terms in the given sequence is -167165.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
