Which one of the basic functions linear, quadratic, rational,exponential is

[cristina g]

related to the arithmetic series?

[Wal C]

quadraticBecause Sn = n/2(2a + (n - 1)d)= (2a - d)/2 n + d/2 n² (a quadratic in n)Where:a = first termd = common differencen = number of terms of the sequence being summed in the seriesRemember also that a series is different to a sequence as the series is generated by summing a sequenceSo an arithmetic SEQUENCE is linearie Un = a + (n - 1) d = dn + (a - d)There is an associated SERIES S1, S2, S3, ... Sn, ...where Sn = U1 + U2 + U3 + .... + Unand this is the basis of my original solution ie quadratic

[masteroftheobvious]

Arithmetic sequences are ones where the next term is related to the previous one by adding or subtracting, e.g. 1,2,3,4 or 2,4,6,8.Arithmetic series are sums of arithmetic sequences.Looking at the simple example 1,2,3,4, we see that the sequence values are 1, 3, 6, 10....or in general, "triangular" numbers, where the nth term is n*(n+1)/2, or 1/2 n2, for a quadratic function.p.s. sorry about the confusion on sequence vs. series