Identify the pattern or rule for each sequence and .
For , observe the pattern: each term is multiplied by to get the next term. Thus, .
For , observe the pattern: each term decreases by 15. Thus, .
Calculate using the formula for : .
Calculate using the formula for : .
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sequences
A sequence is an ordered list of numbers that follow a specific pattern or rule. In this question, the sequences {a_n}, {b_n}, and {c_n} are defined by their respective terms. Understanding how to identify the pattern in each sequence is crucial for calculating specific terms, such as a10 and b10.
Sequences can be classified as arithmetic or geometric based on their patterns. An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio. Recognizing the type of sequence helps in deriving a formula for the nth term, which is essential for finding a10 and b10 in this problem.
Summation involves adding together specific terms from sequences. In this case, the task is to find the sum of the 10th terms from two sequences, a10 and b10. Understanding how to compute these terms accurately and then perform the addition is key to solving the problem.