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Sequenses

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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?

Aug 26, 2018

#1
+391
+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

Aug 26, 2018

#1
+391
+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
#3
+1114
+1