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# arithmetic sequences

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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?

Dec 22, 2020

### Best Answer

#1
+1

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

Dec 23, 2020

### 1+0 Answers

#1
+1
Best Answer

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

hectictar Dec 23, 2020