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Find the 500-th term of an arithmetic sequence with {eq}a_1 = 6.9 \text{ and } d = 0.3 {/eq}.

Question:

Find the 500-th term of an arithmetic sequence with {eq}a_1 = 6.9 \text{ and } d = 0.3 {/eq}.

Arithmetic Sequence

An arithmetic sequence is a sequence in which each term and its previous term have the same difference. This difference is known as the common difference. Since we know the first term and the common difference in the question we can find the nth term of the sequence by using the formula,

{eq}a_n = a_1 + (n-1)d {/eq}, where {eq}a_n {/eq} is the {eq}n^{th} {/eq} term and {eq}d {/eq} is a common difference.

Answer and Explanation: 1

Now, here we can use the formula {eq}a_n = a_1 + (n-1)d {/eq}, where {eq}a_n {/eq} is the {eq}n^{th} {/eq} term and {eq}d {/eq} is the common difference to find the value of the 500-th term.

Thus, we have,

{eq}a_n = a_1 + (n-1)d\\ a_{500} = 6.9 + (n-1)0\\ a_{500} = 6.9 {/eq}

Thus the 500-th term is 0.


Learn more about this topic:

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Arithmetic Sequence: Formula & Definition

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Chapter 26 / Lesson 3
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Discover the arithmetic sequence definition and how math uses it. Know its formula and how to solve problems relating to it through sample calculations.


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