find the sum of the first 10 terms of the arithmetic sequence 4,10,16,20,28,......

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yvie15 @yvie15

October 2022 1 2 Report

find the sum of the first 10 terms of the arithmetic sequence 4,10,16,20,28,...

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KAntoineDoix

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✒️SERIES

$••••••••••••••••••••••••••••••••••••••••••••••••••$

$\large\underline{\mathbb{PROBLEM}:}$

Find the sum of the first 10 terms of the arithmetic sequence 4,10,16,22,28,...

$••••••••••••••••••••••••••••••••••••••••••••••••••$

$\large\underline{\mathbb{ANSWER}:}$

$\qquad \Large \:\: \rm{S_{10} = 310}$

$••••••••••••••••••••••••••••••••••••••••••••••••••$

$\large\underline{\mathbb{SOLUTION}:}$

» Determine the common difference.

$d = a_2 - a_1 = 10 - 4 = 6$

$d = a_3 - a_2 = 16 - 10 = 6$

$d = a_4 - a_3 = 22 - 16 = 6$

» Determine the sum of the first ten terms of the sequence using the arithmetic series formula.

$\begin{align} & \bold{Formula:} \\ & \boxed{\rm S_n = \frac{\,n\,}{2} \big[ 2a_1 + d(n-1) \big]} \end{align}$

$S_{10} = \frac{10}{2} \big[ 2(4) + 6(10-1) \big] \\$

$S_{10} = \frac{10}{2} \big[ 2(4) + 6(9) \big] \\$

$S_{10} = 5 \big[ 8 + 54 \big]$

$S_{10} = 5 \big[ 62 \big]$

$S_{10} = 310$

$\therefore$ The sum of the first ten terms of the arithmetic sequence is 310

$••••••••••••••••••••••••••••••••••••••••••••••••••$

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yvie15 thank you so much

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✒️SERIES

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