Given the arithmetic series a 1 + a 2 + a 3 + a 4 a1+a2+a3+a4 14 + 18 + 22 + 26 + . . + 86 what is the value of sum?

950

Step-by-step explanation:

The common difference is 4, so the general term can be written:

... an = 14 + 4(n -1)

The value of n for the last term is ...

... 86 = 14 + 4(n -1) . . . . . the computation for the last term, 86

... 72 = 4(n -1) . . . . . . . . . subtract 14

... 18 = n -1 . . . . . . . . . . . divide by 4

... 19 = n . . . . . . . . . . . . . add 1

Your series has 19 terms. The first term is 14 and the last is 86, so the average term is (14+86)/2 = 50. Since there are 19 terms, the sum of them is ...

... 19×50 = 950