Two arithmetic sequences A and B both begin with 30 and have common differences of absolute value 10, 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?

Lightning
Aug 26, 2018

#1**+2 **

Arithmetic sequence \(A\), starts at 30, and goes up 10 each step.

Arithmetic sequence \(B\), starts at 30, and goes down 10 each step.

To find the \(n\)th term of a sequenece, we have a formula: \(a + (n-1)d\), where \(a\) is the first number of the sequence and \(d\) is the difference between each term. Let's use this formula to find the \(51\)st term of sequence \(A\).

We have \(30 + (51-1)10= 30 + 50\times10 = 30+500=530\).

For sequence \(B\), we have \(30 + (51-1)(-10) = 30 + 50(-10) = 30 + -500 = -470\).

So, the difference would be \(530 - (-470) = 530 + 470 = 1000\).

- Daisy

dierdurst
Aug 26, 2018

#1**+2 **

Best Answer

Arithmetic sequence \(A\), starts at 30, and goes up 10 each step.

Arithmetic sequence \(B\), starts at 30, and goes down 10 each step.

To find the \(n\)th term of a sequenece, we have a formula: \(a + (n-1)d\), where \(a\) is the first number of the sequence and \(d\) is the difference between each term. Let's use this formula to find the \(51\)st term of sequence \(A\).

We have \(30 + (51-1)10= 30 + 50\times10 = 30+500=530\).

For sequence \(B\), we have \(30 + (51-1)(-10) = 30 + 50(-10) = 30 + -500 = -470\).

So, the difference would be \(530 - (-470) = 530 + 470 = 1000\).

- Daisy

dierdurst
Aug 26, 2018