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Find the sum of a finite arithmetic sequence from n = 1 to n = 13, using the expression 3n + 3.

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The sum of an arithmetic sequence is the average of the first and last terms time the number of terms...

So the first term is 3+3 and the last term is 3(13)+3

So the sum is:

13(6+42)/2

312
User Sankarann
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Answer:

The sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.

Explanation:

The given expression is


3n+3

For n=1,


3(1)+3=6

For n=2,


3(2)+3=9

For n=3,


3(3)+3=12

The required AP is


6, 9, 12, ...

Here first term is 6 and common difference is 3.

The sum of n terms of an AP is


S_n=(n)/(2)[2a+(n-1)d]


S_(13)=(13)/(2)[2(6)+(13-1)(3)]


S_(13)=(13)/(2)[12+36]


S_(13)=312

Therefore the sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.

User Avaneep
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