Examine the number pattern and answer the following questions:
960, 860, 760, 660.....
Answer (2)
The number pattern decreases by 100 each time, starting from 960. The next numbers in the sequence are 560 and 460. The nth term can be found using the formula a n = 960 − 100 ( n − 1 ) .
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To find the pattern in the sequence given, we examine the numbers: 960, 860, 760, 660.
Identify the Pattern:
Start from the first number, 960.
The next number is 860. To find the difference between the two numbers, subtract: 960 - 860 = 100.
Continue to the next number: 860 - 760 = 100.
Finally, go from 760 to 660: 760 - 660 = 100.
Define the Pattern:
The pattern consists of each number being decreased by 100.
This is a linear pattern or sequence where the common difference is -100.
Equation of the Sequence:
If you want to find the nth term in the sequence, the formula for an arithmetic sequence is given by: a n = a 1 + ( n − 1 ) d where a 1 is the first term, n is the term number, and d is the common difference.
For this sequence: a 1 = 960 and d = − 100 .
Therefore, the formula becomes a n = 960 + ( n − 1 ) ( − 100 ) .
Example of Finding a Term:
To find the fifth term, substitute n = 5 into the formula: a 5 = 960 + ( 5 − 1 ) ( − 100 ) a 5 = 960 − 400 a 5 = 560
The terms of this sequence decrease by 100 each step.
