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Find the 9 th term of the arithmetic sequence
4x+7,9x+10,14 x+13,dots
Answer:

Find the $9$ th term of the arithmetic sequence $4 x+7,9 x+10,14 x+13, \ldots$ $\newline$ Answer:

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Solve exponential equations using logarithms

Full solution

Q. Find the

9

th term of the arithmetic sequence

4 x+7,9 x+10,14 x+13, \ldots

\newline

Answer:

Find Common Difference: Identify the common difference of the arithmetic sequence. $\newline$ The common difference $d$ is the difference between any two consecutive terms. $\newline$ For the given sequence, we can find the common difference by subtracting the first term from the second term. $\newline$ $d = (9x + 10) - (4x + 7)$ $\newline$ $d = 9x - 4x + 10 - 7$ $\newline$ $d = 5x + 3$
First Term: Determine the first term of the sequence. $\newline$ The first term $a_1$ is given as $4x + 7$ .
Use nth Term Formula: Use the formula for the nth term of an arithmetic sequence to find the $9^{\text{th}}$ term. $\newline$ The nth term ( $a_n$ ) of an arithmetic sequence is given by the formula: $\newline$ $a_n = a_1 + (n - 1)d$ $\newline$ We want to find the $9^{\text{th}}$ term ( $a_9$ ), so we will substitute $n$ with $9$ . $\newline$ $a_9 = (4x + 7) + (9 - 1)(5x + 3)$
Simplify for $9$ th Term: Simplify the expression to find the $9$ th term. $\newline$ $a_9 = (4x + 7) + 8(5x + 3)$ $\newline$ $a_9 = (4x + 7) + (40x + 24)$ $\newline$ $a_9 = 4x + 7 + 40x + 24$ $\newline$ $a_9 = 44x + 31$

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f(x) = 6x

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f(x) = 6^x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

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