In Exercises 57–62, let
{a_n} = - 5, 10, - 20, 40, ...,
{b_n} = 10, - 5, - 20, - 35, ...,
{c_n} = - 2, 1, - 1/2, 1/4
Find the difference between the sum of the first 10 terms of {an} and the sum of the first 10 terms of {bn}.
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1
Identify the pattern or rule for each sequence {a_n} and {b_n}.
Determine the general formula for the nth term of each sequence.
Calculate the sum of the first 10 terms for the sequence {a_n} using the formula for the sum of a sequence.
Calculate the sum of the first 10 terms for the sequence {b_n} using the formula for the sum of a sequence.
Find the difference between the sum of the first 10 terms of {a_n} and the sum of the first 10 terms of {b_n}.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Arithmetic Sequences
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference. Understanding how to identify and calculate the terms of an arithmetic sequence is crucial for solving problems involving sums of sequences.
The summation of a series involves adding a sequence of numbers together. For arithmetic sequences, the sum of the first n terms can be calculated using the formula S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term. This concept is essential for finding the total of the first 10 terms in the given sequences.
The difference of sums refers to the process of subtracting one sum from another. In this context, it involves calculating the sum of the first 10 terms of two different sequences and then finding the difference between these two sums. This concept is key to arriving at the final answer for the problem.