1+5+9+\cdots+85 Write the arithmetic series in summation not

NompsypeFeplk

NompsypeFeplk

Answered question

2021-11-18

1+5+9++85
Write the arithmetic series in summation notation.

Answer & Explanation

Kevin Hunt

Kevin Hunt

Beginner2021-11-19Added 20 answers

Step 1
sequence and series:
Arithmetic sequence:
Let a,a+d,a+2d,a+(n1)d be an arithmetic sequence then,
an=a+(n1)d, where a is the first term and d is the common difference
(i.e,d=(a+d)(a)=(a+2d)(a+d)
Solution:
consider the series
1+5+9++85
Series (1) is an arithmetic series.
Reason, [a=1,d=51=95=4.d=4] (common sialfo).
Arithmetic sequence,
nth term an=a+(n1)d
where a is the first term
d is the common difference
Thus, general term of (1),
an=a+(n1)d
=1+(n1)(4)
=1+4n4=4n3
an=4n3
and an=85 (from (1)).
i.e. 4n3=85
4n=88
n=22
Hence, 1+5+9++85=n=122(4n3)
Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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