We can add, subtract, multiply, and divide two sequences by performing the operation on the terms with the same index. Ex: {ai} = {i2} = {(cid:1005), (cid:1008), (cid:1013), (cid:1005)(cid:1010), } {bi} = {(cid:1007)i} = {(cid:1007), (cid:1010), (cid:1013), (cid:1005)(cid:1006), } {ai + bi} = {i2 + (cid:1007)i} = {(cid:1008), (cid:1005)(cid:1004), (cid:1005)(cid:1012), (cid:1006)(cid:1012), } Also the constant k{ai} = {kai} where every term is multiplied by the constant k. 8{ai} = {8i2} = {(cid:1012), (cid:1007)(cid:1006), (cid:1011)(cid:1006), (cid:1005)(cid:1006)(cid:1012), } We often find ourselves given several terms of the sequence and we want to find a general formula which describes that sequence. Ex: {ai} = {(cid:1004), (cid:1005), (cid:1008), (cid:1013), (cid:1005)(cid:1010), } We could write {ai} = {i2}i = 0. An alternating sequence is one in which consecutive terms have different signs. We normally represent this mathematically by including a factor of (-1)i or (-1)i + 1. Since this is an alternating sequence, consider instead the corresponding absolute sequence:
