+1246 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?
+400 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 nth 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 51st term of sequence A.
We have 30+(51−1)10=30+50×10=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
+400 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 nth 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 51st term of sequence A.
We have 30+(51−1)10=30+50×10=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
