Sum of the sequence is -22407
What is arithmetic sequence ?
An arithmetic sequence is a sequence where the common difference between two consecutive terms are always same.
If a be the first term and d be the common difference of a arithmetic sequence, then n th term of it = [tex]a_{n}[/tex] = a+(n-1)d
Sum of n terms = [tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex](2a+(n-1)d)
How to solve the given sum ?
GIven sequence is 9+4+(-1)+.......+(-471)
First we arrange the sequence in right sequence.
(-471)+................(-1)+4+9
Now, we have to find the value n,
Here a = -471
So, nth term 9, common difference = 5
So, [tex]a_{n}[/tex] = [tex]a\\[/tex]+(n-1)d
⇒ [tex]a_{n}[/tex]-[tex]a[/tex]=(n-1)5
⇒ 9+(-471)=5(n-1)
⇒ 480=5n-5
⇒ 5n = 485
⇒ n = 97
So, sum of terms = [tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex](2a+(n-1)d)
= [tex]\frac{97}{2}[/tex](-942+(96×5))
= [tex]\frac{97}{2}[/tex](-942+480)
= [tex]\frac{97}{2}[/tex]×(-462)
= -22407
Hence, The sum is -22407.
Learn more about arithmetic sequence here :
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