What is the sum of the arithmetic sequence 152, 138, 124 if there are 24 terms?

Wendy Larsen

Wendy Larsen

Answered question

2023-01-05

What is the sum of the arithmetic sequence 152, 138, 124 if there are 24 terms?

Answer & Explanation

Myncboyncgm6

Myncboyncgm6

Beginner2023-01-06Added 8 answers

An arithmetic sequence's general term can be expressed in the following way:
an=a+d(n1)
where d is the common difference and a is the initial term.
Therefore:
2n=1Nan=n=1N(an+aN+1n)
2n=1Nan=n=1N(a+d(n1)+a+d(Nn))
2n=1Nan=n=1N(2a+dNd)
2n=1Nan=N(2a+dNd)
So:
sN=n=1Nan=12N(2a+dNd)
Equivalently, the sum of the first #N# terms of an arithmetic sequence is the number of terms multiplied by the average term.
Then:
sN=Na1+aN2
sN=12N(a+d(11)+a+d(N1))
sN=12N(2a+dNd)
For our example:
a=152
d=138152=14
N=24
So:
s24=12(24)(2(152)+(14)(24)14)
s24=12(304336+14)
s24=12(18)
s24=216

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