Two arithmetic sequences A and B both begin with 30 and have common differences of absolute value 18, with sequence A increasing and sequence B decreasing. What is the absolute value of the difference between the 51st term of sequence A and the 51st term of sequence B?
+9479 I'm not totally sure, but here's my guess:
Sequence A is: 30, 48, 66, 84, 102, 120, . . .
Sequence B is: 30, 12, -6, -24, -42, -60, . . .
So we can say
A1 = 30 = 30 + 18*0
A2 = 48 = 30 + 18*1
A3 = 66 = 30 + 18*2
A4 = 84 = 30 + 18*3
An = 30 + 18*(n - 1)
B1 = 30 = 30 - 18*0
B2 = 12 = 30 - 18*1
B3 = -6 = 30 - 18*2
Bn = 30 - 18*(n - 1)
And so..
The 51st term of sequence A = A51 = 30 + 18*(51 - 1) = 30 + 18*50 = 930
The 51st term of sequence B = B51 = 30 - 18*(51 - 1) = 30 - 18*50 = -870
The absolute value of the difference between A51 and B51 = | 930 - -870 | = 1800
+9479 I'm not totally sure, but here's my guess:
Sequence A is: 30, 48, 66, 84, 102, 120, . . .
Sequence B is: 30, 12, -6, -24, -42, -60, . . .
So we can say
A1 = 30 = 30 + 18*0
A2 = 48 = 30 + 18*1
A3 = 66 = 30 + 18*2
A4 = 84 = 30 + 18*3
An = 30 + 18*(n - 1)
B1 = 30 = 30 - 18*0
B2 = 12 = 30 - 18*1
B3 = -6 = 30 - 18*2
Bn = 30 - 18*(n - 1)
And so..
The 51st term of sequence A = A51 = 30 + 18*(51 - 1) = 30 + 18*50 = 930
The 51st term of sequence B = B51 = 30 - 18*(51 - 1) = 30 - 18*50 = -870
The absolute value of the difference between A51 and B51 = | 930 - -870 | = 1800
