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What is the sum of the series 3,---5,-13..........-229

User Dvilela
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ANSWER


S_(30)= - 3390

Step-by-step explanation

The given sequence is

3,-5,-13,.....-229.

The first term of this sequence is

a_1=3

There is a common difference of


d = - 5 - 3 = - 8

The last term of this sequence is -229.

The nth term of this sequence is given by:


a_n=a_1+d(n-1)

We use the last term to determine the number of terms in the sequence.


- 229 = 3 + - 8(n - 1)


- 229 - 3= - 8(n - 1)


- 232= - 8(n - 1)

Divide through by -8;


29= (n - 1)


n = 30

Hence there are thirty terms in the sequence.

The sum of the first n terms is given by:


S_n= (n)/(2) ( a_(1) + l)

The sum of the first 30 terms is given by:


S_(30)= (30)/(2) ( 3 + - 229)


S_(30)=15( - 226)


S_(30)= - 3390

User Girish Dusane
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