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The first four terms of the sequences with \( n \)th term of \( 5 n-4 \) are

Ask by Haynes Collins. in South Africa
Feb 21,2025

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The first four terms of the sequence are 1, 6, 11, and 16.

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Simplify the expression by following steps: - step0: Solution: \(5n-4\) Calculate or simplify the expression \( 5*3-4 \). Calculate the value by following steps: - step0: Calculate: \(5\times 3-4\) - step1: Multiply the numbers: \(15-4\) - step2: Subtract the numbers: \(11\) Calculate or simplify the expression \( 5*2-4 \). Calculate the value by following steps: - step0: Calculate: \(5\times 2-4\) - step1: Multiply the numbers: \(10-4\) - step2: Subtract the numbers: \(6\) Calculate or simplify the expression \( 5*4-4 \). Calculate the value by following steps: - step0: Calculate: \(5\times 4-4\) - step1: Multiply the numbers: \(20-4\) - step2: Subtract the numbers: \(16\) Calculate or simplify the expression \( 5*1-4 \). Calculate the value by following steps: - step0: Calculate: \(5\times 1-4\) - step1: Multiply: \(5-4\) - step2: Subtract the numbers: \(1\) To find the first four terms of the sequence defined by the \( n \)th term \( 5n - 4 \), we can calculate the values for \( n = 1, 2, 3, \) and \( 4 \). 1. For \( n = 1 \): \[ 5(1) - 4 = 5 - 4 = 1 \] 2. For \( n = 2 \): \[ 5(2) - 4 = 10 - 4 = 6 \] 3. For \( n = 3 \): \[ 5(3) - 4 = 15 - 4 = 11 \] 4. For \( n = 4 \): \[ 5(4) - 4 = 20 - 4 = 16 \] Thus, the first four terms of the sequence are: \[ 1, 6, 11, 16 \]

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The first four terms of the sequence generated by the formula \( 5n - 4 \) can be found by substituting \( n \) with the values 1 through 4. For \( n = 1 \): \( 5(1) - 4 = 1 \) For \( n = 2 \): \( 5(2) - 4 = 6 \) For \( n = 3 \): \( 5(3) - 4 = 11 \) For \( n = 4 \): \( 5(4) - 4 = 16 \) Thus, the first four terms of the sequence are 1, 6, 11, and 16. Now, isn't it fascinating how a simple linear equation generates a sequence that increases uniformly? Just like building blocks, these terms stack up by a constant difference of 5! Each term is simply the previous term plus 5, revealing the beauty of arithmetic sequences. What’s even cooler? You can apply this formula in real-world scenarios, like predicting the total cost of buying multiple items at a fixed price, where each item corresponds to a value of \( n \). For instance, if one item costs $1, the cost for two items is $6, for three it's $11, and for four it's $16. Math is everywhere!

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