Arithmetic Number Sequences. How To Work Out The Sum Of The First n Terms In An Arithmetic Sequence.

In this video you will be shown how to sum an arithmetic sequence. The formula to use is S=1/2n(2a+(n-1)d). S stands for the sum, a is the first term of the sequence and d is the common difference. The common difference can be found by subtracting the first term from the second term.

So in example 1 you are asked to find the sum of the first 20 terms in the arithmetic sequence 4,7,10,13,16. The first term is 10 so a=10, the common difference is 3 so d=3, and the number of terms to sum is 20 so n=20. Substituting these numbers into the formula gives S=1/2(20)(2(4)+(20-1)(3)), so S = 10(8+57)=650. So the sum of the first 20 terms in the sequence is 650.