In a sequence of 6 numbers every number after the first two is the average of the previous number. the 4th number in the sequence is 22 and the 6th number in the sequence is 45 determine all 6 numbers in the sequence

298, -70, 114, 22, 68, 45 Let's start with our initial sequence. a, b, c, 22, e, 45 Since the average of 22 and e is equal to 45, we have (22 + e)/2 = 45 22 + e = 90 e = 68 So our sequence is now a, b, c, 22, 68, 45 And since 68 is the average of c and 22, we have 68 = (c + 22)/2 136 = c + 22 114 = c So our sequence is now a, b, 114, 22, 68, 45 And b becomes 22 = (b + 114)/2 44 = b + 114 -70 = b So our sequence is now a, -70, 114, 22, 68, 45 And finally, for a, we have 114 = (-70 + a)/2 228 = -70 + a 298 = a So the final sequence becomes 298, -70, 114, 22, 68, 45