Write the pattern rule for:
(i) 64, 32, 16, 8, 4, ...
(ii) 2, 10, 50, 250, ...
(iii) 2500, 2250, 2000, 1750, ...
Answer (2)
The pattern rules for the sequences are as follows: (i) divide by 2, (ii) multiply by 5, and (iii) subtract 250. Each rule consistently transforms one term into the next. Recognizing these patterns allows for easier continuation of the sequences.
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In examining the sequences provided, we need to identify pattern rules that describe how each sequence progresses. Let's analyze each sequence one by one:
(i) 64, 32, 16, 8, 4, ...
This sequence is a geometric sequence with a constant ratio between consecutive terms.
What is happening? Each term is divided by 2 (or multiplied by 2 1 ).
Why this pattern? If you take any term and divide it by 2, you get the next term.
Pattern Rule : The nth term of the sequence can be found using the formula: a n = 64 × ( 2 1 ) n − 1 , where n is the position of the term in the sequence (starting from n = 1 ).
(ii) 2, 10, 50, 250, ...
This sequence is also a geometric sequence.
What is happening? Each term is multiplied by 5 to get the next term.
Why this pattern? You multiply 2 by 5 to get 10, 10 by 5 to get 50, and so on.
Pattern Rule : The nth term of the sequence can be found using the formula: a n = 2 × 5 n − 1 .
(iii) 2500, 2250, 2000, 1750, ...
This sequence is an arithmetic sequence with a constant difference between consecutive terms.
What is happening? Each term decreases by 250 to get the next term.
Why this pattern? Subtracting 250 from a term gives the next term in the sequence.
Pattern Rule : The nth term of the sequence can be found using the formula: a n = 2500 − 250 × ( n − 1 ) .
Breaking down the patterns helps in predicting future terms and understanding the nature of sequences.
