How Do I Find The Partial Sum Of An Arithmetic Sequence

The partial sum of an arithmetic sequence can be found using the formula ##S=n/2(a1+an)## where n= the number of terms, a1= the value of the first term, and an= the value of the last (nth) term.

As an example, if you were to find the partial sum of the sequence 1, 3, 5, 7, 9, …, 49, you would first need to determine that there are 25 terms, a1= 1 and an=49. ##25/2(1+49) = 625##.

Another example might ask you to find the sum of the first 20 terms of the sequence 8, 13, 18, 23, … To find an, you could use the formula ##an=dn+a0## where d= the common difference and a0 = the 0th term, or the term before the first term in the sequence. So ##an=5*20+3 = 103##. Therefore ##S=20/2(8+103) = 1110##.

Here’s a video from my YouTube channel (www.YouTube.com/MrDaveEbert) with another example:

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