What is the sum of the arithmetic sequence 22, 13, 4?

1 Answer
Sep 27, 2014

22 + 13 + 4 = 3922+13+4=39. A very straightforward answer.

However, if one wishes to find it that way (the stupid way), then first notice that this is a simple arithmetic series. Use the formula S = n/2 (a_1 + a_{\text{n}))S=n2(a1+an) or the formula S = n/2 (2a_1 + (n-1)d)S=n2(2a1+(n1)d) where a_1a1 is the first term, a_nan is the last term, dd is the common difference, nn is the number of terms in your series.

Note that both of these are equivalent since a_n = a_1 + (n- 1)dan=a1+(n1)d.

S = 3/2 (22 + 4) = 39S=32(22+4)=39 or S = 3/2 ( 2\cdot 22 - 9\cdot 2) = 39.S=32(22292)=39.